Search result: Catalogue data in Autumn Semester 2017

Agricultural Sciences Bachelor Information
Bachelor Studies (Programme Regulations 2016)
1. Semester
First Year Examinations
NumberTitleTypeECTSHoursLecturers
401-0251-00LMathematics IO6 credits4V + 2UL. Halbeisen
AbstractThis course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.
ObjectiveMathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment.

The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses.
Content1. Single-Variable Calculus:
review of differentiation, linearisation, Taylor polynomials, maxima and minima, antiderivative, fundamental theorem of calculus, integration methods, improper integrals.

2. Linear Algebra and Complex Numbers:
systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra.

3. Ordinary Differential Equations:
separable ordinary differential equations (ODEs), integration by substitution, 1st and 2nd order linear ODEs, homogeneous systems of linear ODEs with constant coefficients, introduction to 2-dimensional dynamical systems.
Literature- Thomas, G. B.: Thomas' Calculus, Part 1 (Pearson Addison-Wesley).
- Bretscher, O.: Linear Algebra with Applications (Pearson Prentice Hall).
Prerequisites / NoticePrerequisites: familiarity with the basic notions from Calculus, in particular those of function and derivative.

Mathe-Lab (Assistance):
Mondays 12-14, Tuesdays 17-19, Wednesdays 17-19, in Room HG E 41.
Basic Courses (Second Year)
Examination Block
NumberTitleTypeECTSHoursLecturers
701-0071-00LMathematics III: Systems AnalysisO4 credits2V + 1UN. Gruber, M. Vogt
AbstractThe objective of the systems analysis course is to deepen and illustrate the mathematical concepts on the basis of a series of very concrete examples. Topics covered include: linear box models with one or several variables, non-linear box models with one or several variables, time-discrete models, and continuous models in time and space.
ObjectiveLearning and applying of concepts (models) and quantitative methods to address concrete problems of environmental relevance. Understanding and applying the systems-analytic approach, i.e., Recognizing the core of the problem - simplification - quantitative approach - prediction.
ContentLink
Lecture notesOverhead slides will be made available through Ilias.
LiteratureImboden, D.S. and S. Pfenninger (2013) Introduction to Systems Analysis: Mathematically Modeling Natural Systems. Berlin Heidelberg: Springer Verlag.

Link
Bachelor Studies (Programme Regulations 2010)
5. Semester
Methodical Courses
NumberTitleTypeECTSHoursLecturers
751-0441-00LScientific Analysis and Presentation of DataO2 credits2GW. Eugster
AbstractThis lecture gives an introduction to the scientific work with data covering all steps from data entry via statistical analyses to producing correct scientific graphical output. Exercises with the data analysis software R (via RStudio) will provide hands-on opportunities to get acquainted with data analysis and presentation. Field data gathered with Prof. E. Frossard will be used.
ObjectiveThis lecture with exercises gives an introduction to the scientific work with data, starting with data acquisition and ending with statistical analyses as they are often required for a bachelor thesis (descriptive statistics, linear regression etc.). Getting data organized with a spreadsheet program (LibreOffice, Excel) and then transfering them to the open-source R package will be the primary focus. An imporant aspect will be to learn which graphical representation of data are best suited for the task (how can data be presented clearly and still scientifically correct?)
ContentTentative Programme:
1. Introduction
2. Data acquisition, data organization, data storage, working with data
3. Graphical presentations I - Spreadsheets
4. Preparation of own data from field course with Prof. E. Frossard / 4. Sem.
5. Correct and problematic graphical data displays
6. Introduction to 'R'
7. Data import and graphical presentation
8. Statistical distribution and confidence intervals
9. Statistical tests - Repetition and hands-on applications
10. Linear regressions
11./12. Analysis of Variance
13. ANOVA - Discussion of results with Prof. E. Frossard

Last week of semester: examination (Leistungskontrolle)
Lecture notesMainly German (with some English passages from text books)
Prerequisites / NoticeTheoretical background in ensemble statistics from the mandatory course in the 4th semester; students should have cleared the examination of that fundamental course to be able to follow
Agroecosystem Sciences Master Information
Master Studies (Programme Regulations 2016)
Major in Agriculture Economics
Methodology Competences
Methods in Agricultural Economics
NumberTitleTypeECTSHoursLecturers
751-0423-00LRisk Analysis and Risk Management in AgricultureW+3 credits2GR. Finger
AbstractAgricultural production is exposed to various risks which are important for decisions taken by farmers and other actors in the agri-food sector. Moreover, risk management is indispensable for all actors. This course introduces modern concepts on decision making under risk and recent developments in risk management. The focus of this course in on agriculture applications.
Objective-to develop a better understanding of decision making under uncertainty and risk;
-to gain experience in different approaches to analyze risky decisions;
-to develop an understanding for different sources of risk in agricultural production;
-to understand the crucial role of subjective perceptions and preferences for risk management decisions;
-to get an overview on risk management in the agricultural sector, with a particular focus on insurance solutions
Content- Quantification and measurement of risk
- Risk preferences, expected utility theory and alternative models of risk behavior
- Concepts on the decision making under risk
- Production, investment and diversification decisions under risk
- Risk management in agriculture
Lecture notesHandouts will be distributed in the lecture and available on the moodle.
Prerequisites / Noticeknowledge of basic concepts of probability theory and microeconomics
Minors
Agricultural Economics and Policy
NumberTitleTypeECTSHoursLecturers
751-0423-00LRisk Analysis and Risk Management in AgricultureW3 credits2GR. Finger
AbstractAgricultural production is exposed to various risks which are important for decisions taken by farmers and other actors in the agri-food sector. Moreover, risk management is indispensable for all actors. This course introduces modern concepts on decision making under risk and recent developments in risk management. The focus of this course in on agriculture applications.
Objective-to develop a better understanding of decision making under uncertainty and risk;
-to gain experience in different approaches to analyze risky decisions;
-to develop an understanding for different sources of risk in agricultural production;
-to understand the crucial role of subjective perceptions and preferences for risk management decisions;
-to get an overview on risk management in the agricultural sector, with a particular focus on insurance solutions
Content- Quantification and measurement of risk
- Risk preferences, expected utility theory and alternative models of risk behavior
- Concepts on the decision making under risk
- Production, investment and diversification decisions under risk
- Risk management in agriculture
Lecture notesHandouts will be distributed in the lecture and available on the moodle.
Prerequisites / Noticeknowledge of basic concepts of probability theory and microeconomics
Master Studies (Programme Regulations 2011)
Majors
Major in Food and Resource Use Economics
Methodology Competences
Methods in Food and Resource Use Economics
NumberTitleTypeECTSHoursLecturers
751-0423-00LRisk Analysis and Risk Management in AgricultureW+3 credits2GR. Finger
AbstractAgricultural production is exposed to various risks which are important for decisions taken by farmers and other actors in the agri-food sector. Moreover, risk management is indispensable for all actors. This course introduces modern concepts on decision making under risk and recent developments in risk management. The focus of this course in on agriculture applications.
Objective-to develop a better understanding of decision making under uncertainty and risk;
-to gain experience in different approaches to analyze risky decisions;
-to develop an understanding for different sources of risk in agricultural production;
-to understand the crucial role of subjective perceptions and preferences for risk management decisions;
-to get an overview on risk management in the agricultural sector, with a particular focus on insurance solutions
Content- Quantification and measurement of risk
- Risk preferences, expected utility theory and alternative models of risk behavior
- Concepts on the decision making under risk
- Production, investment and diversification decisions under risk
- Risk management in agriculture
Lecture notesHandouts will be distributed in the lecture and available on the moodle.
Prerequisites / Noticeknowledge of basic concepts of probability theory and microeconomics
Atmospheric and Climate Science Master Information
Modules
Hydrology and Water Cycle
NumberTitleTypeECTSHoursLecturers
701-1253-00LAnalysis of Climate and Weather Data Information W3 credits2GC. Frei
AbstractObservation networks and numerical climate and forcasting models deliver large primary datasets. The use of this data in practice and in research requires specific techniques of statistical data analysis. This lecture introduces a range of frequently used techniques, and enables students to apply them and to properly interpret their results.
ObjectiveObservation networks and numerical climate and forcasting models deliver large primary datasets. The use of this data in practice and in research requires specific techniques of statistical data analysis. This lecture introduces a range of frequently used techniques, and enables students to apply them and to properly interpret their results.
ContentIntroduction into the theoretical background and the practical application of methods of data analysis in meteorology and climatology.

Topics: exploratory methods, hypothesis testing, analysis of climate trends, measuring the skill of climate and forecasting models, analysis of extremes, principal component analysis and maximum covariance analysis.

The lecture also provides an introduction into R, a programming language and graphics tool frequently used for data analysis in meteorology and climatology. During hands-on computer exercises the student will become familiar with the practical application of the methods.
Lecture notesDocumentation and supporting material include:
- documented view graphs used during the lecture
- excercise sets and solutions
- R-packages with software and example datasets for exercise sessions

All material is made available via the lecture web-page.
LiteratureSuggested literature:
- Wilks D.S., 2005: Statistical Methods in the Atmospheric Science. (2nd edition). International Geophysical Series, Academic Press Inc. (London)
- Coles S., 2001: An introduction to statistical modeling of extreme values. Springer, London. 208 pp.
Prerequisites / NoticePrerequisites: Atmosphäre, Mathematik IV: Statistik, Anwendungsnahes Programmieren.
Minors
Minor in Sustainable Energy Use
NumberTitleTypeECTSHoursLecturers
227-1631-00LEnergy System Analysis Information W4 credits3GG. Hug, S. Hellweg, F. Noembrini, A. Schlüter
AbstractThe course provides an introduction to the methods and tools for analysis of energy consumption, energy production and energy flows. Environmental aspects are included as well as economical considerations. Different sectors of the society are discussed, such as electric power, buildings, and transportation. Models for energy system analysis planning are introduced.
ObjectiveThe purpose of the course is to give the participants an overview of the methods and tools used for energy systems analysis and how to use these in simple practical examples.
ContentThe course gives an introduction to methods and tools for analysis of energy consumption, energy production and energy flows. Both larger systems, e.g. countries, and smaller systems, e.g. industries, homes, vehicles, are studied. The tools and methods are applied to various problems during the exercises. Different conventions of energy statistics used are introduced.

The course provides also an introduction to energy systems models for developing scenarios of future energy consumption and production. Bottom-up and Top-Down approaches are addressed and their features and applications discussed.

The course contains the following parts:
Part I: Energy flows and energy statistics
Part II: Environmental impacts
Part III: Electric power systems
Part IV: Energy in buildings
Part V: Energy in transportation
Part VI: Energy systems models
Lecture notesHandouts
LiteratureExcerpts from various books, e.g. K. Blok: Introduction to Energy Analysis, Techne Press, Amsterdam 2006, ISBN 90-8594-016-8
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
701-0071-AALMathematics III: Systems Analysis
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-4 credits9RN. Gruber
AbstractThe objective of the systems analysis course is to deepen and illustrate the mathematical concepts on the basis of a series of very concrete examples. Topics covered include: linear box models with one or several variables, non-linear box models with one or several variables, time-discrete models, and continuous models in time and space.
ObjectiveLearning and applying of concepts (models) and quantitative methods to address concrete problems of environmental relevance. Understanding and applying the systems-analytic approach, i.e., Recognizing the core of the problem - simplification - quantitative approach - prediction.
ContentLink
Lecture notesOverhead slides will be made available through Ilias.
LiteratureImboden, D.S. and S. Pfenninger (2013) Introduction to Systems Analysis: Mathematically Modeling Natural Systems. Berlin Heidelberg: Springer Verlag.

Link
701-1901-AALSystems Analysis
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-4 credits9RN. Gruber
AbstractSystems analysis is about the application of mathematical concepts to solve real world problems in a quantitative manner. Areas covered include: Dynamic linear models with one and several variables, Non-linear models with one or several variables; discrete-time models; and continuous models in space and time.
ObjectiveThe goal of the course is to develop quantitative skills in order to understand and solve a range of typical environmental problems.
ContentThe subject of the exam is the content of my
undergraduate lecture series Systemanalyse I and II (see Link).
This course is closely aligned with the Imboden&Koch / Imboden&Pfenniger books, except that I essentially skip chapter 7.
Lecture notesNo script is available, but you can purchase the Imboden/Koch or Imboden/Pfenniger books (or download some of the chapters yourself) through the Springer Verlag:

English version:
Link

German version:
Link
Civil Engineering Bachelor Information
Bachelor Studies (Programme Regulations 2014)
First Year Compulsory Courses
First Year Examinations
In place of the German course 851-0703-03L Introduction to Law for Civil Engineering students can take the French course 851-0709-00L Droit civil.
NumberTitleTypeECTSHoursLecturers
401-0241-00LAnalysis I Information O7 credits5V + 2UM. Akka Ginosar
AbstractMathematical tools for the engineer
ObjectiveMathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers.
ContentComplex numbers.
Calculus for functions of one variable with applications.
Simple Mathematical models in engineering.
Lecture notesDie Vorlesung folgt weitgehend

Klaus Dürrschnabel, "Mathematik für Ingenieure - Eine Einführung mit Anwendungs- und Alltagsbeispielen", Springer; online verfügbar unter:
Link
LiteratureNeben Klaus Dürrschnabel, "Mathematik für Ingenieure - Eine Einführung mit Anwendungs- und Alltagsbeispielen", Springer sind auch die folgenden Bücher/Skripte empfehlenswert und decken den zu behandelnden Stoff ab:

Tilo Arens et al., "Mathematik", Springer; online verfügbar unter:
Link

Meike Akveld, "Analysis 1", vdf;
Link

Urs Stammbach, "Analysis I/II" (erhältlich im ETH Store);
Link
Compulsory Courses 3. Semester
Examination Block 1
NumberTitleTypeECTSHoursLecturers
401-0243-00LAnalysis IIIO3 credits2V + 1UA. Sisto
AbstractWe will model and solve scientific problems with partial differential equations. Differential equations which are important in applications will be classified and solved. Elliptic, parabolic and hyperbolic differential equations will be treated. The following mathematical tools will be introduced: Laplace and Fourier transforms, Fourier series, separation of variables, methods of characteristics.
ObjectiveLearning to model scientific problems using partial differential equations and developing a good command of the mathematical methods that can be applied to them. Knowing the formulation of important problems in science and engineering with a view toward civil engineering (when possible). Understanding the properties of the different types of partial differential equations arising in science and in engineering.
ContentClassification of partial differential equations

Study of the Heat equation general diffusion/parabolic problems using the following tools:
* Separation of variables
* Fourier series
* Fourier transform
* Laplace transform

Study of the wave equation and general hyperbolic problems using similar tools and the method of characteristics.

Study of the Laplace equation and general elliptic problems using similar tools and generalizations of Fourier series.
LiteratureThe course material is taken from the following sources:

Stanley J. Farlow - Partial Differential Equations for Scientists and Engineers

G. Felder: Partielle Differenzialgleichungen.
Link
Prerequisites / NoticeAnalysis I and II. In particular, knowing how to solve ordinary differential equations is an important prerequisite.
Civil Engineering Master Information
1. Semester
Major Courses
Major in Structural Engineering
NumberTitleTypeECTSHoursLecturers
101-0187-00LStructural Reliability and Risk Analysis Information W3 credits2GS. Marelli
AbstractStructural reliability aims at quantifying the probability of failure of systems due to uncertainties in their design, manufacturing and environmental conditions. Risk analysis combines this information with the consequences of failure in view of optimal decision making. The course presents the underlying probabilistic modelling and computational methods for reliability and risk assessment.
ObjectiveThe goal of this course is to provide the students with a thorough understanding of the key concepts behind structural reliability and risk analysis. After this course the students will have refreshed their knowledge of probability theory and statistics to model uncertainties in view of engineering applications. They will be able to analyze the reliability of a structure and to use risk assessment methods for decision making under uncertain conditions. They will be aware of the state-of-the-art computational methods and software in this field.
ContentEngineers are confronted every day to decision making under limited amount of information and uncertain conditions. When designing new structures and systems, the design codes such as SIA or Euro- codes usually provide a framework that guarantees safety and reliability. However the level of safety is not quantified explicitly, which does not allow the analyst to properly choose between design variants and evaluate a total cost in case of failure. In contrast, the framework of risk analysis allows one to incorporate the uncertainty in decision making.

The first part of the course is a reminder on probability theory that is used as a main tool for reliability and risk analysis. Classical concepts such as random variables and vectors, dependence and correlation are recalled. Basic statistical inference methods used for building a probabilistic model from the available data, e.g. the maximum likelihood method, are presented.

The second part is related to structural reliability analysis, i.e. methods that allow one to compute probabilities of failure of a given system with respect to prescribed criteria. The framework of reliability analysis is first set up. Reliability indices are introduced together with the first order-second moment method (FOSM) and the first order reliability method (FORM). Methods based on Monte Carlo simulation are then reviewed and illustrated through various examples. By-products of reliability analysis such as sensitivity measures and partial safety coefficients are derived and their links to structural design codes is shown. The reliability of structural systems is also introduced as well as the methods used to reassess existing structures based on new information.

The third part of the course addresses risk assessment methods. Techniques for the identification of hazard scenarios and their representation by fault trees and event trees are described. Risk is defined with respect to the concept of expected utility in the framework of decision making. Elements of Bayesian decision making, i.e. pre-, post and pre-post risk assessment methods are presented.

The course also includes a tutorial using the UQLab software dedicated to real world structural reliability analysis.
Lecture notesSlides of the lectures are available online every week. A printed version of the full set of slides is proposed to the students at the beginning of the semester.
LiteratureAng, A. and Tang, W.H, Probability Concepts in Engineering - Emphasis on Applications to Civil and Environmental Engineering, 2nd Edition, John Wiley & Sons, 2007.

S. Marelli, R. Schöbi, B. Sudret, UQLab user manual - Structural reliability (rare events estimation), Report UQLab-V0.92-107.
Prerequisites / NoticeBasic course on probability theory and statistics
3. Semester
Major Courses
Major in Construction and Maintenance Management
NumberTitleTypeECTSHoursLecturers
101-0439-00LIntroduction to Economic Analysis - A Case Study Approach with Cost Benefit Analysis in Transport
Remark:
Former Title "Introduction to Economic Policy - A Case Study Approach with Cost Benefit Analysis in Transport".
W6 credits4GK. W. Axhausen, R. Schubert
AbstractThe course presents basic economic principles as well as cost benefit analyses in transport; it also introduces methods used to derive the monetary values of non-market goods.
ObjectiveFamiliarity with basic microeconomic and macroeconomic principles and with the essential methods of project appraisal
ContentBasic microeconomic and macroeconomic üpronciples; Cost-Benefit-Analyses; multi-criteria analyses; European guidelines; stated response methods; travel cost approach and others; Valuation of travel time savings; valuation of traffic safety
Lecture notesmoodle platform for the basic economic principles; handouts
LiteratureTaylor, M.P., Mankiw, N.G. (2014): Economics; Harvard Press

VSS (2006) SN 640 820: Kosten-Nutzen-Analysen im Strassenverkehr, VSS, Zürich.

Boardman, A.E., D.H. Greenberg, A.R. Vining und D.L. Weimer (2001) Cost – Benefit – Analysis: Concepts and Practise, Prentice-Hall, Upper Saddle River.

ecoplan and metron (2005) Kosten-Nutzen-Analysen im Strassenverkehr: Kommentar zu SN 640 820, UVEK, Bern.
Major in Structural Engineering
NumberTitleTypeECTSHoursLecturers
101-0179-00LProbabilistic Seismic Risk Analysis and Management for Civil Systems
Does not take place this semester.
W3 credits2GB. Stojadinovic, to be announced
AbstractAdvanced topics covered in this course are: 1) probabilistic seismic hazard analysis; 2) probabilistic seismic risk analysis; 3) seismic risk management using structural and financial engineering means; and, time permitting, 4) advanced topics in systemic probabilistic risk evaluation.
ObjectiveAfter successfully completing this course the students will be able to:

1. Gather the necessary data and conduct a probabilistic seismic hazard analysis for a site.
2. Gather the necessary data and conduct a probabilistic vulnerability analysis of a building or an element of a civil infrastructure system at a site.
3. Design structural and/or financial engineering solutions to mitigate the seismic risk at a site.
ContentThis course extends the series of two courses on seismic design of structures at ETHZ and introduces the topic of probabilistic seismic risk analysis and seismic risk management for the build environment and civil infrastructure systems. The following advanced topics will be covered in this course: 1) probabilistic seismic hazard analysis; 2) probabilistic seismic risk analysis; 3) seismic risk management using structural and financial engineering means; and, time permitting, 4) advanced topics in systemic probabilistic risk evaluation.
Lecture notesThe electronic copies of the learning material will be uploaded to ILIAS and available through myStudies. This will include the lecture notes, additional reading, and exercise problems and solutions. There is no textbook for this course.
LiteratureReading material:
- Jack R Benjamin, C. Allin Cornell (2014) Probability, Statistics, and Decision for Civil Engineers
- A. H-S. Ang (Author), W. H. Tang Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering
- P.E. Pinto, R. Giannini and P. Franchin (2004) Seismic reliability analysis of structures, IUSSPress. Pavia;
- McGuire, R.K. 2004. Seismic hazard and risk analysis: EERI Monograph MNO-10, Earthquake Engineering Research Institute.
- A Mc. Neil, R. Frey and P. Embrechts, Quantitative Risk Management, Concepts, Techniques and Tools, Princeton University Press, 2015
- R. Rees, A. Wambach, The Microeconomics of Insurance, Foundations and Trends in Microeconomics, Vol. 4, Mps. 1-2 (2008), pp. 1- 163, DOI: 10.1561/0700000023
- Earthquake Engineering: From Engineering Seismology to Performance-Based Engineering, Yousef Borzorgnia and Vitelmo Bertero, Eds., CRC Press, 2004
- Dynamics of Structures: Theory and Applications to Earthquake Engineering, 4th edition, Anil Chopra, Prentice Hall, 2012
- Erdbebensicherung von Bauwerken, 2nd edition, Hugo Bachmann, Birkhäuser, Basel, 2002

References:
-Norm SIA 261: Einwirkungen auf Tragwerke (Actions on Structures). Schweizerischer Ingenieur- und Architekten-Verein, Zürich, 2003

Software:
- Bispec: software for unidirectional and bidirectional dynamic time-history and spectral seismic analysis of a simple dynamic system. Link
- SAP2000 v15.1: general-purpose 3D nonlinear structural analysis software. Link
- OpenSees: Open System for Earthquake Engineering Simulation, is an object-oriented, open- source software framework. Link
Prerequisites / NoticeETH Seismic Design of Structures I course (101-0188-00), or equivalent. Students are expected to understand the seismological nature of earthquakes, to characterize the ground motion excitation, to analyze the response of elastic single- and multiple-degree-of-freedom systems to earthquake excitation, to use the concept of response and design spectrum, to compute the equivalent seismic loads on simple structures, and to perform code-based seismic design of simple structures.
Major in Transport Systems
NumberTitleTypeECTSHoursLecturers
101-0439-00LIntroduction to Economic Analysis - A Case Study Approach with Cost Benefit Analysis in Transport
Remark:
Former Title "Introduction to Economic Policy - A Case Study Approach with Cost Benefit Analysis in Transport".
W6 credits4GK. W. Axhausen, R. Schubert
AbstractThe course presents basic economic principles as well as cost benefit analyses in transport; it also introduces methods used to derive the monetary values of non-market goods.
ObjectiveFamiliarity with basic microeconomic and macroeconomic principles and with the essential methods of project appraisal
ContentBasic microeconomic and macroeconomic üpronciples; Cost-Benefit-Analyses; multi-criteria analyses; European guidelines; stated response methods; travel cost approach and others; Valuation of travel time savings; valuation of traffic safety
Lecture notesmoodle platform for the basic economic principles; handouts
LiteratureTaylor, M.P., Mankiw, N.G. (2014): Economics; Harvard Press

VSS (2006) SN 640 820: Kosten-Nutzen-Analysen im Strassenverkehr, VSS, Zürich.

Boardman, A.E., D.H. Greenberg, A.R. Vining und D.L. Weimer (2001) Cost – Benefit – Analysis: Concepts and Practise, Prentice-Hall, Upper Saddle River.

ecoplan and metron (2005) Kosten-Nutzen-Analysen im Strassenverkehr: Kommentar zu SN 640 820, UVEK, Bern.
Biology Bachelor Information
2. Year, 3. Semester
Core Courses
NumberTitleTypeECTSHoursLecturers
551-1003-00LMethods of Biological Analysis Information O3 credits3GR. Aebersold, M. Badertscher, K. Weis
Abstract529-1042-00
Principles of the most important separation techniques and the interpretation of molecular spectra.

551-1003-00
The course will teach the basis and typical applications of methods for the analysis of nucleic acid sequences, mass spectrometric analysis of proteins and proteomes and advanced light and fluorescent imaging methods.
Objective529-1042-00
Knowledge of the necessary basics and the possibilities of application of the relevant spectroscopical and separation methods in analytical chermistry.

551-1003-00
Knowledge of the theoretical basis of the methods for nucleic acid sequence analysis, mass spectrometry based protein and proteome analysis and advanced light and fluorescent imaging methods, and an understanding of the application of these principles in experimental biology.
Content529-1042-00
Application oriented basics of instrumental analysis in organic chemistry and the empirical employment of the methods of structure elucidation (mass spectrometry, NMR-, IR-, UV/VIS spectroscopy). Basics and application of chromatographic and electrophoretic separation methods. Application of the knowledge by practising.

551-1003-00
The course will consist of lectures covering the theoretical and technical base of the respective analytical methods and of exercises where typical applications of the methods in modern experimental biology are discussed.
Lecture notes529-1042-00
A comprehensive script is available in the HCI-Shop. A summary of the part "Spektroskopie" defines the relevant material for the exam.

551-1003-00
Materials supporting the lectures and exercises will be made available via Moodle.
Literature529-1042-00
- Pretsch E., Bühlmann P., Badertscher M. Structure Determination of Organic Compounds, 5th revised and enlarged English edition, Springer-Verlag, Berlin 2009;
- Pretsch E., Bühlmann P., Badertscher M., Spektroskopische Daten zur Strukturaufklärung organischer Verbindungen, fünfte Auflage, Springer-Verlag, Berlin 2010;
- D.A. Skoog, J.J. Leary, Instrumentelle Analytik, Grundlagen, Geräte, Anwendungen, Springer, Berlin, 1996;
- K. Cammann, Instrumentelle Analytische Chemie, Verfahren, Anwendungen, Qualitätssicherung, Spektrum Akademischer Verlag, Heidelberg, 2001;
- R. Kellner, J.-M. Mermet, M. Otto, H.M. Widmer, Analytical Chemistry, Wiley-VCH Verlag, Weinheim, 1998;
- K. Robards, P.R.Haddad, P.E. Jackson, Principles and practice of modern chromatographic methods, Academic Press, London, 1994;
Prerequisites / Notice529-1042-00
Prerequisites:
- 529-1001-01 V "Allgemeine Chemie I (für Biol./Pharm.Wiss.)"
- 529-1001-00 P "Allgemeine Chemie I (für Biol./Pharm.Wiss.)"
- 529-1011-00 G "Organische Chemie I (für Biol./Pharm.Wiss.)"
3. Year, 5. Semester
Block Courses
Registration for Block courses is mandatory. Please register under Link . Registration period: from 24.7.2017 to 6.8.2017.
Block Courses in 2nd Quarter of the Semester
From 12.10.2017 08:00 Uhr to 3.11.2017 17:00 hr
NumberTitleTypeECTSHoursLecturers
551-1201-00LComputational Methods in Genome and Sequence Analysis Restricted registration - show details
Number of participants limited to 5.

The enrolment is done by the D-BIOL study administration.
W6 credits7GA. Wutz
AbstractThis course aims to provide students with a comprehensive overview of computational methods for sequence analysis and assist with developing skills for application of computational approaches by experimental scientists in the life sciences.
ObjectiveMethods for analyzing animal genomes are increasingly becoming important for applications in human health and biotechnology suggesting that the experience will be useful to develop relevant expertise for a broad range of functions. Students will have the opportunity to advance their knowledge in programming by focusing on algorithms for genome and gene sequence analysis. A major goal of the course will be to lead the student to an independent and empowered attitude towards computational problems. For reaching this goal the students will work on an implementation of a solution for a set real-world problem in genome and sequence analysis under guided supervision.
Content•Understanding the information in biological sequences and quantifying similarity
•Introduction to algorithms for sequence comparison and searches
•Implementation of sequence comparisons and searches in Python
•Accessing data formats associated with genome sequence analysis tasks
•Understanding the anatomy of a real world sequence analysis project
•Applying tools for sequence alignment and estimating error rates
•Ability to implement a solution to a problem in sequence analysis using Python
•Accessing genome annotation and retrieving relevant information in Pandas
•Application of Genomic intervals and arrays for sequence analysis with HTSeq

The course will consist of a series of lectures, assignments for implementing elementary tasks in Python, project development and discussion workshops, and 3 and a half week of practical work implementing a Pythons script as a solution to a real world problem associated with sequence analysis. At the end of the course students will explain their solutions and demonstrate the functionality of their implementations, which will then be discussed and commented on by the group. It is expected that students will be able to apply the knowledge to improve on concrete problems.
Prerequisites / Notice- It is recommended to bring your own computer with a Python installation to the course
- simple computers can be provided
- Programming basics with Python
Block Courses in 4th Quarter of the Semester
From 30.11.2017 08:00 hr to 22.12.2017 17:00 hr
NumberTitleTypeECTSHoursLecturers
551-1417-00LIn Vivo Cryo-EM Analysis of Dynein Motor Proteins Restricted registration - show details
Number of participants limited to 3.

The enrolment is done by the D-BIOL study administration.
W6 credits7GT. Ishikawa
AbstractMotor proteins convert chemical energy into mechanical motion. In this block course, we study dynein motor proteins in cilia. Dynein causes conformational change upon ATP hydrolysis and finally generate ciliary bending motion. Participants will analyze cryo-EM data of cilia and visualize in vivo 3D structure of dynein to learn how motor proteins function in the cell.
ObjectiveThe goal of this course is to be familiar with structural biology techniques of cryo-electron tomography and single particle cryo-EM studies on motor proteins. The main focus is 3D image analysis of cryo-EM datasets acquired by highest-end microscopes. Participants will learn structure-function relationship at various scales: how the conformational change of motor proteins causes mechanical force and generates cellular motility.
ContentMotor proteins, such as dynein, myosin and kinesin, hydrolyze ATP to ADP and phosphate to convert chemical energy to mechanical motion. Their function is essential for intracellular transport, muscle contraction and other cellular motility as well as cell division. Motor proteins have been major targets of biophysical studies. There exist questions from atomic to tissue levels – how ATP hydrolysis causes conformational change of motor proteins; how their motion is regulated by calcium, phosphorylation and other factors; how motions of multiple motor proteins are coordinated to generate cellular motility. Structural biology has been playing central roles to answer these questions. X-ray crystallography and single particle cryo-EM address structural analysis at atomic resolution and try to reveal molecular mechanism of conformational change. Cryo-electron tomography analyze localization and 3D structure of motor proteins in the cell to explain how motions of molecular motors happen in the context of cellular environment and are integrated into cellular motion.
In this course, we study dyneins in cilia. Cilia are force-generating organelles, made by nine microtubules and thousands of dyneins. Dynein hydrolyzes ATP and undergoes conformational change, generating linear motion with respect to the microtubule. As a whole system, cilia integrate motions of these dyneins and orchestrate beating motion. To explain ciliary motion at molecular level, we need to know dynein conformational change in the cellular context. Cryo-electron tomography is recently developed technique to study molecular structures in vivo and therefore a suitable method to study dynein in cilia. Recently spatial resolution of these cryo-EM techniques was dramatically improved, driven by development of new types of detectors and electron optics.
The participants of this course will learn a program to analyze cryo-electron tomography and single particle cryo-EM data, acquired by highest-end electron microscopes and detectors in ETH and other places, and reconstruct 3D structure (tomogram) of cilia from various organisms (from green algae to human). They will further learn a program to study molecular structures from these tomograms (called subtomogram averaging) and apply it to reconstruct high-resolution 3D structure of dyneins, microtubules and regulatory proteins. This practical course is therefore mainly computational, but we will also provide students a chance of cilia preparation from green algae, cryo-EM data collection using an electron microscope in PSI and site-visit of highest-end electron microscope facility in ETH.
Lecture notesScripts will be distributed during the course.
LiteratureAn overview is given in the following review articles. Further literature will be indicated during the course.
Ishikawa (2017) “Axoneme structure from motile cilia” Cold Spring Harb. Perspect Biol. 9. doi: 10.1101/cshperspect.a028076.
Ishikawa (2017) “Cryo-electron tomography of motile cilia and flagella” Cilia 4, 3. doi: 10.1186/s13630-014-0012-7.
Biology Master Information
Elective Major Subject Areas
Elective Major: Ecology and Evolution
Elective Compulsory Master Courses
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
401-6215-00LUsing R for Data Analysis and Graphics (Part I) Information W1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the first part an introduction to the statistical software R for scientists. Topics covered are data generation and selection, graphical and basic statistical functions, creating simple functions, basic types of objects.
ObjectiveThe students will be able to use the software R for simple data analysis.
ContentThe course provides the first part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part I of the course covers the following topics:
- What is R?
- R Basics: reading and writing data from/to files, creating vectors & matrices, selecting elements of dataframes, vectors and matrices, arithmetics;
- Types of data: numeric, character, logical and categorical data, missing values;
- Simple (statistical) functions: summary, mean, var, etc., simple statistical tests;
- Writing simple functions;
- Introduction to graphics: scatter-, boxplots and other high-level plotting functions, embellishing plots by title, axis labels, etc., adding elements (lines, points) to existing plots.

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link

Note: Part I of UsingR is complemented and extended by Part II, which is offered during the second part of the semester and which can be taken independently from Part I.
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeThe course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
401-6217-00LUsing R for Data Analysis and Graphics (Part II) Information W1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the second part an introduction to the statistical software R for scientists. Topics are data generation and selection, graphical functions, important statistical functions, types of objects, models, programming and writing functions.
Note: This part builds on "Using R... (Part I)", but can be taken independently if the basics of R are already known.
ObjectiveThe students will be able to use the software R efficiently for data analysis.
ContentThe course provides the second part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part II of the course builds on part I and covers the following additional topics:
- Elements of the R language: control structures (if, else, loops), lists, overview of R objects, attributes of R objects;
- More on R functions;
- Applying functions to elements of vectors, matrices and lists;
- Object oriented programming with R: classes and methods;
- Tayloring R: options
- Extending basic R: packages

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeBasic knowledge of R equivalent to "Using R .. (part 1)" ( = 401-6215-00L ) is a prerequisite for this course.

The course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
701-1419-00LAnalysis of Ecological DataW3 credits2GS. Güsewell
AbstractThis class provides students with an overview of techniques for data analysis used in modern ecological research, as well as practical experience in running these analyses with R and interpreting the results. Topics include linear models, generalized linear models, mixed models, model selection and randomization methods.
ObjectiveStudents will be able to:
- describe the aims and principles of important techniques for the analysis of ecological data
- choose appropriate techniques for given problems and types of data
- evaluate assumptions and limitations
- implement the analyses in R
- represent the relevant results in graphs, tables and text
- interpret and evaluate the results in ecological terms
Content- Linear models for experimental and observational studies
- Model selection
- Introduction to likelihood inference and Bayesian statistics
- Analysis of counts and proportions (generalised linear models)
- Models for non-linear relationships
- Grouping and correlation structures (mixed models)
- Randomisation methods
Lecture notesLecture notes and additional reading will be available electronically a few days before the course
LiteratureSuggested books for additional reading (available electronically)
Zuur A, Ieno EN & Smith GM (2007) Analysing ecological data. Springer, Berlin.
Zuur A, Ieno EN, Walker NJ, Saveliev AA & Smith GM (2009) Mixed effects models and extensions in ecology with R. Springer, New York.
Faraway JJ (2006) Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. Taylor & Francis.
Prerequisites / NoticeTime schedule
The course takes place on Mondays 12:45-15:00 from 25 September until 27 November, with the final exam on Monday 4 December. The last two weeks of the semester are free.

Prerequisites
- Basic statistical training (e.g. Mathematik IV in D-USYS): Data distributions, descriptive statistics, hypothesis testing, linear regression, analysis of variance
- Basic experience in data handling and data analysis in R

Individual preparation
Students without the required knowledge are asked to contact the lecturer before the first lecture date for support with individual preparation.
Elective Major: Structural Biology and Biophysics
Elective Compulsory Master Courses
NumberTitleTypeECTSHoursLecturers
401-6215-00LUsing R for Data Analysis and Graphics (Part I) Information W1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the first part an introduction to the statistical software R for scientists. Topics covered are data generation and selection, graphical and basic statistical functions, creating simple functions, basic types of objects.
ObjectiveThe students will be able to use the software R for simple data analysis.
ContentThe course provides the first part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part I of the course covers the following topics:
- What is R?
- R Basics: reading and writing data from/to files, creating vectors & matrices, selecting elements of dataframes, vectors and matrices, arithmetics;
- Types of data: numeric, character, logical and categorical data, missing values;
- Simple (statistical) functions: summary, mean, var, etc., simple statistical tests;
- Writing simple functions;
- Introduction to graphics: scatter-, boxplots and other high-level plotting functions, embellishing plots by title, axis labels, etc., adding elements (lines, points) to existing plots.

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link

Note: Part I of UsingR is complemented and extended by Part II, which is offered during the second part of the semester and which can be taken independently from Part I.
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeThe course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
Biomedical Engineering Master Information
Track Courses
Bioelectronics
Recommended Elective Courses
These courses are particularly recommended for the Bioelectronics track. Please consult your track advisor if you wish to select other subjects.
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Bioimaging
Track Core Courses
During the Master program, a minimum of 12 CP must be obtained from track core courses.
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Recommended Elective Courses
These courses are particularly recommended for the Bioimaging track. Please consult your track advisor if you wish to select other subjects.
NumberTitleTypeECTSHoursLecturers
227-0391-00LMedical Image Analysis
Does not take place this semester.
W3 credits2GE. Konukoglu
AbstractIt is the objective of this lecture to introduce the basic concepts used
in Medical Image Analysis. In particular the lecture focuses on shape
representation schemes, segmentation techniques, and the various image registration methods commonly used in Medical Image Analysis applications.
ObjectiveThis lecture aims to give an overview of the basic concepts of Medical Image Analysis and its application areas.
Prerequisites / NoticeBasic knowledge of computer vision would be helpful.
227-0969-00LMethods & Models for fMRI Data Analysis Information W6 credits4VK. Stephan
AbstractThis course teaches methods and models for fMRI data analysis, covering all aspects of statistical parametric mapping (SPM), incl. preprocessing, the general linear model, statistical inference, multiple comparison corrections, event-related designs, and Dynamic Causal Modelling (DCM), a Bayesian framework for identification of nonlinear neuronal systems from neurophysiological data.
ObjectiveTo obtain in-depth knowledge of the theoretical foundations of SPM
and DCM and of their application to empirical fMRI data.
ContentThis course teaches state-of-the-art methods and models for fMRI data analysis. It covers all aspects of statistical parametric mapping (SPM), incl. preprocessing, the general linear model, frequentist and Bayesian inference, multiple comparison corrections, and event-related designs, and Dynamic Causal Modelling (DCM), a Bayesian framework for identification of nonlinear neuronal systems from neurophysiological data. A particular emphasis of the course will be on methodological questions arising in the context of studies in psychiatry, neurology and neuroeconomics.
Biomechanics
Track Core Courses
During the Master program, a minimum of 12 CP must be obtained from track core courses.
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Medical Physics
Other Elective Courses
These courses may be suitable for the Medical Physics track. Please consult your track advisor.
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Biotechnology Master Information
Master Studies (Programme Regulations 2017)
Practical Training
Students need to acquire a total of 14 ECTS in lab courses.
All listed lab courses are mandatory.
NumberTitleTypeECTSHoursLecturers
636-0201-00LLab Course: Methods in Cell Analysis and Laboratory Automation Restricted registration - show details
Only for Biotechnology MSc, Programme Regulations 2017.
O2 credits6PT. Horn
AbstractThe course Methods in Cell Analysis and Laboratory Automation introduces students to high-end cell analysis and sample preparation methods including image analysis. Students will be taught theoretical aspects and skills in Flow Cytometry, Light Microscopy, Image Analysis, and the use of Laboratory Automation.
Objective-to understand the technical and physical principles of light microscopes and flow cytometers
-to have hands-on experience in the use of these technologies to analyze/image real samples
-to be able to run a basic analysis of the data and images obtained with flow cytometers and microscopes
-to get introduced to liquid handling (pipetting) robotics and learn how to implement a basic workflow
ContentThe practical course will have five units at 2 days each (total 10 days):
1. Flow Cytometry:
a. Introduction to Flow Cytometry
b. Practical demonstration on flow cytometry analyzers and flow cytometry cell sorters
c. Flow cytometry sample preparation
d. Learn how to use flow cytometry equipment to analyze and sort fluorescence-labeled cells
2. Light microscopy
a. Learn how to build a microscope and understand the underlying physical principles
b. Learn how to use a modern automated wide field fluorescence microscope
c. Use this microscope to automatically acquire images of a cell culture assay to analyze the dose-dependent effect of a drug treatment
3. Image Analysis
a. Introduction to the fundamentals of image analysis
b. Learn the basics of the image analysis software Fiji/ImageJ
c. Use Fiji/ImageJ to analyze the images acquired during the microscopy exercise
4. Laboratory Automation
a. Introduction to the basics of automated liquid handling/ lab robotics
b. See examples on using lab automation for plasmid library generation and cell cultivation
c. Learn how to program and execute a basic pipetting workflow including liquid handling and labware transfers on Tecan and Hamilton robotic systems
5. Presentations
a. Each student will be assigned to an individual topic of the course and will have to prepare a presentation on it.
b. Presentations and discussion in form of a Colloquium
Lecture notesYou will find further information on the practical course and the equipment at:
Link
Link
LiteratureMicroscopy: Murphy and Davidson, Fundamentals of Light Microscopy and Electronic Imaging, John Wiley & Sons, 2012
Flow Cytometry: Shapiro, Practical Flow Cytometry, John Wiley & Sons, 2005
Image analysis: R. C. Gonzalez, R. E. Woods, Digital Image Processing (3rd Edition), Prentice Hall
Laboratory Automation: Design and construction of a first-generation high-throughput integrated robotic molecular biology platform for bioenergy applications (2011) J. Lab. Autom., 16(4), 292-307
Prerequisites / NoticeThe following knowledge is required for the course:
-basic laboratory methods
-basic physics of optics (properties of light, refraction, lenses, fluorescence)
-basic biology of cells (cell anatomy and physiology)
CAS in Applied Statistics Information
Course duration: about 12 months

Next course: FS 2019
Compulsory Courses
NumberTitleTypeECTSHoursLecturers
447-0625-01LApplied Analysis of Variance and Experimental Design I Restricted registration - show details
Only for DAS and CAS in Applied Statistics.
O3 credits1V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Further Courses
NumberTitleTypeECTSHoursLecturers
447-0625-02LApplied Analysis of Variance and Experimental Design II Restricted registration - show details
Only for DAS and CAS in Applied Statistics.
Z3 credits1V + 1UL. Meier
AbstractRandom effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze sophisticated experiments in the fields of natural sciences. They will gain practical experience by using the software R.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
CAS in Development and Cooperation Information
Module
NumberTitleTypeECTSHoursLecturers
865-0000-06LImpact Analysis: Methods and Applications.
Only for MAS/CAS in Development and Cooperation students, as well as specialists with at least 24 months of practical experience in international cooperation.
Doctoral students dealing with empirical research in the area of development and cooperation (EZA) may be admitted "sur Dossier".

Registration only through the NADEL administration office.
W2 credits3GI. Günther
AbstractThe course gives an introduction to the most important methods for rigorous impact analysis of development programs and projects. The course is designed to both cover the most fundamental methods of impact analysis and introduce real world case studies from national, international and non-governmental development organizations and asks how rigorous impact analysis has influenced their policies.
ObjectiveParticipants understand the most important methods of impact analysis. They are able to conduct small scale studies to evaluate the impact of their own programs as well as manage larger impact evaluations for their organizations. Participants are able to use the results of own and external impact studies.
ContentIntroduction to rigorous impact analysis; Case studies and their policy implications; Introduction to the required statistical knowledge; Potentials and limitations of quantitative analysis; Experimental and quasi-experimental methods; Relevant and feasible indicators for the measurement of outcomes and impacts; Data collection and analysis; Project management of an impact analysis.
Prerequisites / NoticeStudents of the course must fulfil requirements specified on the homepage of NADEL. Electronic registration may be done only after registration with NADEL secretariate.
Chemistry Bachelor Information
1. Semester
Compulsory Subjects First Year Examinations
NumberTitleTypeECTSHoursLecturers
401-0271-00LMathematical Foundations I: Analysis AO5 credits3V + 2UL. Kobel-Keller
AbstractIntroduction to calculus in one dimension. Building simple models and analysing them mathematically.
Functions of one variable: the notion of a function, of the derivative, the idea of a differential equation, complex numbers, Taylor polynomials and Taylor series. The integral of a function of one variable.
ObjectiveIntroduction to calculus in one dimension. Building simple models and analysing them mathematically.
ContentFunctions of one variable: the notion of a function, of the derivative, the idea of a differential equation, complex numbers, Taylor polynomials and Taylor series. The integral of a function of one variable.
LiteratureG. B. Thomas, M. D. Weir, J. Hass: Analysis 1, Lehr- und Übungsbuch, Pearson-Verlag
D. W. Jordan, P. Smith: Mathematische Methoden für die Praxis, Spektrum Akademischer Verlag
R. Sperb/M. Akveld: Analysis I (vdf)
L. Papula: Mathematik für Ingenieure und Naturwissenschaftler (3 Bände), Vieweg
further reading suggestions will be indicated during the lecture
Chemical Engineering Bachelor Information
1. Semester
Compulsory Subjects First Year Examinations
NumberTitleTypeECTSHoursLecturers
401-0271-00LMathematical Foundations I: Analysis AO5 credits3V + 2UL. Kobel-Keller
AbstractIntroduction to calculus in one dimension. Building simple models and analysing them mathematically.
Functions of one variable: the notion of a function, of the derivative, the idea of a differential equation, complex numbers, Taylor polynomials and Taylor series. The integral of a function of one variable.
ObjectiveIntroduction to calculus in one dimension. Building simple models and analysing them mathematically.
ContentFunctions of one variable: the notion of a function, of the derivative, the idea of a differential equation, complex numbers, Taylor polynomials and Taylor series. The integral of a function of one variable.
LiteratureG. B. Thomas, M. D. Weir, J. Hass: Analysis 1, Lehr- und Übungsbuch, Pearson-Verlag
D. W. Jordan, P. Smith: Mathematische Methoden für die Praxis, Spektrum Akademischer Verlag
R. Sperb/M. Akveld: Analysis I (vdf)
L. Papula: Mathematik für Ingenieure und Naturwissenschaftler (3 Bände), Vieweg
further reading suggestions will be indicated during the lecture
Computational Biology and Bioinformatics Master Information
More informations at: Link
Master Studies (Programme Regulations 2017)
Core Courses
Please note that the list of core courses is a closed list. Other courses cannot be added to the core course category in the study plan. Also the assignments of courses to core subcategories cannot be changed.
Students need to pass at least one course in each core subcategory.
A total of 40 ECTS needs to be acquired in the core course category.
Data Science
NumberTitleTypeECTSHoursLecturers
401-6282-00LStatistical Analysis of High-Throughput Genomic and Transcriptomic Data (University of Zurich)
No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH.
UZH Module Code: STA426

Mind the enrolment deadlines at UZH:
Link
W5 credits3GH. Rehrauer, M. Robinson
AbstractA range of topics will be covered, including basic molecular biology, genomics technologies and in particular, a wide range of statistical and computational methods that have been used in the analysis of DNA microarray and high throughput sequencing experiments.
Objective-Understand the fundamental "scientific process" in the field of Statistical Bioinformatics
-Be equipped with the skills/tools to preprocess genomic data (Unix, Bioconductor, mapping, etc.) and ensure reproducible research (Sweave)
-Have a general knowledge of the types of data and biological applications encountered with microarray and sequencing data
-Have the general knowledge of the range of statistical methods that get used with microarray and sequencing data
-Gain the ability to apply statistical methods/knowledge/software to a collaborative biological project
-Gain the ability to critical assess the statistical bioinformatics literature
-Write a coherent summary of a bioinformatics problem and its solution in statistical terms
ContentLectures will include: microarray preprocessing; normalization; exploratory data analysis techniques such as clustering, PCA and multidimensional scaling; Controlling error rates of statistical tests (FPR versus FDR versus FWER); limma (linear models for microarray analysis); mapping algorithms (for RNA/ChIP-seq); RNA-seq quantification; statistical analyses for differential count data; isoform switching; epigenomics data including DNA methylation; gene set analyses; classification
Lecture notesLecture notes, published manuscripts
Prerequisites / NoticePrerequisites: Basic knowlegde of the programming language R, sufficient knowledge in statistics

Former course title: Statistical Methods for the Analysis of Microarray and Short-Read Sequencing Data
Master Studies (Programme Regulations 2011)
Core Courses
NumberTitleTypeECTSHoursLecturers
401-6282-00LStatistical Analysis of High-Throughput Genomic and Transcriptomic Data (University of Zurich)
No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH.
UZH Module Code: STA426

Mind the enrolment deadlines at UZH:
Link
W5 credits3GH. Rehrauer, M. Robinson
AbstractA range of topics will be covered, including basic molecular biology, genomics technologies and in particular, a wide range of statistical and computational methods that have been used in the analysis of DNA microarray and high throughput sequencing experiments.
Objective-Understand the fundamental "scientific process" in the field of Statistical Bioinformatics
-Be equipped with the skills/tools to preprocess genomic data (Unix, Bioconductor, mapping, etc.) and ensure reproducible research (Sweave)
-Have a general knowledge of the types of data and biological applications encountered with microarray and sequencing data
-Have the general knowledge of the range of statistical methods that get used with microarray and sequencing data
-Gain the ability to apply statistical methods/knowledge/software to a collaborative biological project
-Gain the ability to critical assess the statistical bioinformatics literature
-Write a coherent summary of a bioinformatics problem and its solution in statistical terms
ContentLectures will include: microarray preprocessing; normalization; exploratory data analysis techniques such as clustering, PCA and multidimensional scaling; Controlling error rates of statistical tests (FPR versus FDR versus FWER); limma (linear models for microarray analysis); mapping algorithms (for RNA/ChIP-seq); RNA-seq quantification; statistical analyses for differential count data; isoform switching; epigenomics data including DNA methylation; gene set analyses; classification
Lecture notesLecture notes, published manuscripts
Prerequisites / NoticePrerequisites: Basic knowlegde of the programming language R, sufficient knowledge in statistics

Former course title: Statistical Methods for the Analysis of Microarray and Short-Read Sequencing Data
DAS in Applied Statistics Information
Course duration: about 20 months

Next course: FS 2019
Compulsory Courses
NumberTitleTypeECTSHoursLecturers
447-0625-01LApplied Analysis of Variance and Experimental Design I Restricted registration - show details
Only for DAS and CAS in Applied Statistics.
O3 credits1V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Electives
NumberTitleTypeECTSHoursLecturers
447-0625-02LApplied Analysis of Variance and Experimental Design II Restricted registration - show details
Only for DAS and CAS in Applied Statistics.
W3 credits1V + 1UL. Meier
AbstractRandom effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze sophisticated experiments in the fields of natural sciences. They will gain practical experience by using the software R.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Data Science Master Information
Core Courses
Core Electives
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
Doctoral Department of Chemistry and Applied Biosciences Information
Further information at: Link
Doctoral and Post-Doctoral Courses
Doctoral Studies in Inorganic Chemistry
NumberTitleTypeECTSHoursLecturers
529-0169-00LInstrumental AnalysisE-0 credits2SD. Günther
AbstractGroup seminar on elemental analysis and isotope ratio determinations using various plasma sources
Objective
ContentDevelopments in plasma mass spectrometry and alternative plasma sources
Doctoral Department of Mechanical and Process Engineering Information
More Information at: Link
Doctoral and Post-Doctoral Courses
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
Doctoral Department of Mathematics Information
More Information at: Link

The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM.
Link
WARNING: Do not mistake ECTS credits for credit points for doctoral studies!
Graduate School
Official website of the Zurich Graduate School in Mathematics:
Link
NumberTitleTypeECTSHoursLecturers
401-4657-00LNumerical Analysis of Stochastic Ordinary Differential Equations Information
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
W6 credits3V + 1UA. Jentzen
AbstractCourse on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.
ObjectiveThe aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.
ContentGeneration of random numbers
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Multilevel Monte Carlo methods for SODEs
Applications to computational finance: Option valuation
Lecture notesLecture Notes are available in the lecture homepage (please follow the link in the Learning materials section).
LiteratureP. Glassermann:
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.

P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
Prerequisites / NoticePrerequisites:

Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.

a) mandatory courses:
Elementary Probability,
Probability Theory I.

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday, September 20, 2017

Date of the End-of-Semester examination: Wednesday, December 20, 2017, 13:00-15:00; students must arrive before 12:30 at ETH HG E 19.
Room for the End-of-Semester examination: ETH HG E 19.

Exam inspection: Monday, March 5, 2018,
13:00-14:00 at HG D 5.1
Please bring your legi.
401-4623-00LTime Series Analysis
Does not take place this semester.
W6 credits3Gnot available
AbstractStatistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R.
ObjectiveUnderstanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.
ContentThis course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations.
Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R.
Lecture notesNot available
LiteratureA list of references will be distributed during the course.
Prerequisites / NoticeBasic knowledge in probability and statistics
Colloquia
NumberTitleTypeECTSHoursLecturers
401-5350-00LAnalysis Seminar Information E-0 credits1KM. Struwe, A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, T. Ilmanen, T. Kappeler, T. Rivière, D. A. Salamon
AbstractResearch colloquium
Objective
Doctoral Department of Environmental Sciences Information
More Information at: Link
Environmental Sciences
Atmosphere and Climate
NumberTitleTypeECTSHoursLecturers
701-1253-00LAnalysis of Climate and Weather Data Information W3 credits2GC. Frei
AbstractObservation networks and numerical climate and forcasting models deliver large primary datasets. The use of this data in practice and in research requires specific techniques of statistical data analysis. This lecture introduces a range of frequently used techniques, and enables students to apply them and to properly interpret their results.
ObjectiveObservation networks and numerical climate and forcasting models deliver large primary datasets. The use of this data in practice and in research requires specific techniques of statistical data analysis. This lecture introduces a range of frequently used techniques, and enables students to apply them and to properly interpret their results.
ContentIntroduction into the theoretical background and the practical application of methods of data analysis in meteorology and climatology.

Topics: exploratory methods, hypothesis testing, analysis of climate trends, measuring the skill of climate and forecasting models, analysis of extremes, principal component analysis and maximum covariance analysis.

The lecture also provides an introduction into R, a programming language and graphics tool frequently used for data analysis in meteorology and climatology. During hands-on computer exercises the student will become familiar with the practical application of the methods.
Lecture notesDocumentation and supporting material include:
- documented view graphs used during the lecture
- excercise sets and solutions
- R-packages with software and example datasets for exercise sessions

All material is made available via the lecture web-page.
LiteratureSuggested literature:
- Wilks D.S., 2005: Statistical Methods in the Atmospheric Science. (2nd edition). International Geophysical Series, Academic Press Inc. (London)
- Coles S., 2001: An introduction to statistical modeling of extreme values. Springer, London. 208 pp.
Prerequisites / NoticePrerequisites: Atmosphäre, Mathematik IV: Statistik, Anwendungsnahes Programmieren.
Electrical Engineering and Information Technology Bachelor Information
1. Semester
First Year Examinations
First Year Examination Block B
NumberTitleTypeECTSHoursLecturers
401-0231-10LAnalysis IO8 credits4V + 3UT. H. Willwacher
AbstractCalculus of one variable: Real and complex numbers, vectors, limits, sequences, series, power series, continuous maps, differentiation and integration in one variable, introduction to ordinary differential equations
ObjectiveEinfuehrung in die Grundlagen der Analysis
Lecture notesKonrad Koenigsberger, Analysis I.
Christian Blatter: Ingenieur-Analysis (Kapitel 1-3)
3. Semester
Examination Blocks
Examination Block 1
NumberTitleTypeECTSHoursLecturers
401-0353-00LAnalysis III Information O4 credits2V + 1UA. Figalli
AbstractIn this lecture we treat problems in applied analysis. The focus lies on the simplest cases of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation and the wave equation.
Objective
Content1.) Klassifizierung von PDE's
- linear, quasilinear, nicht-linear
- elliptisch, parabolisch, hyperbolisch

2.) Quasilineare PDE
- Methode der Charakteristiken (Beispiele)

3.) Elliptische PDE
- Bsp: Laplace-Gleichung
- Harmonische Funktionen, Maximumsprinzip, Mittelwerts-Formel.
- Methode der Variablenseparation.

4.) Parabolische PDE
- Bsp: Wärmeleitungsgleichung
- Bsp: Inverse Wärmeleitungsgleichung
- Methode der Variablenseparation

5.) Hyperbolische PDE
- Bsp: Wellengleichung
- Formel von d'Alembert in (1+1)-Dimensionen
- Methode der Variablenseparation

6.) Green'sche Funktionen
- Rechnen mit der Dirac-Deltafunktion
- Idee der Green'schen Funktionen (Beispiele)

7.) Ausblick auf numerische Methoden
- 5-Punkt-Diskretisierung des Laplace-Operators (Beispiele)
LiteratureY. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005)

Zusätzliche Literatur:
Erwin Kreyszig, "Advanced Engineering Mathematics", John Wiley & Sons, Kap. 8, 11, 16 (sehr gutes Buch, als Referenz zu benutzen)
Norbert Hungerbühler, "Einführung in die partiellen Differentialgleichungen", vdf Hochschulverlag AG an der ETH Zürich.
G. Felder:Partielle Differenzialgleichungen.
Link
Prerequisites / NoticePrerequisites: Analysis I and II, Fourier series (Komplexe Analysis)
Electrical Engineering and Information Technology Master Information
Major Courses
A total of 42 CP must be achieved during the Master Program. The individual study plan is subject to the tutor's approval.
Communication
Recommended Subjects
These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.
NumberTitleTypeECTSHoursLecturers
227-0377-00LPhysics of Failure and Failure Analysis of Electronic Devices and EquipmentW3 credits2VU. Sennhauser
AbstractFailures have to be avoided by proper design, material selection and manufacturing. Properties, degradation mechanisms, and expected lifetime of materials are introduced and the basics of failure analysis and analysis equipment are presented. Failures will be demonstrated experimentally and the opportunity is offered to perform a failure analysis with advanced equipment in the laboratory.
ObjectiveIntroduction to the degradation and failure mechanisms and causes of electronic components, devices and systems as well as to methods and tools of reliability testing, characterization and failure analysis.
ContentSummary of reliability and failure analysis terminology; physics of failure: materials properties, physical processes and failure mechanisms; failure analysis of ICs, PCBs, opto-electronics, discrete and other components and devices; basics and properties of instruments; application in circuit design and reliability analysis
Lecture notesComprehensive copy of transparencies
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Computers and Networks
Recommended Subjects
These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.
NumberTitleTypeECTSHoursLecturers
227-0377-00LPhysics of Failure and Failure Analysis of Electronic Devices and EquipmentW3 credits2VU. Sennhauser
AbstractFailures have to be avoided by proper design, material selection and manufacturing. Properties, degradation mechanisms, and expected lifetime of materials are introduced and the basics of failure analysis and analysis equipment are presented. Failures will be demonstrated experimentally and the opportunity is offered to perform a failure analysis with advanced equipment in the laboratory.
ObjectiveIntroduction to the degradation and failure mechanisms and causes of electronic components, devices and systems as well as to methods and tools of reliability testing, characterization and failure analysis.
ContentSummary of reliability and failure analysis terminology; physics of failure: materials properties, physical processes and failure mechanisms; failure analysis of ICs, PCBs, opto-electronics, discrete and other components and devices; basics and properties of instruments; application in circuit design and reliability analysis
Lecture notesComprehensive copy of transparencies
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Electronics and Photonics
Recommended Subjects
These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.
NumberTitleTypeECTSHoursLecturers
227-0377-00LPhysics of Failure and Failure Analysis of Electronic Devices and EquipmentW3 credits2VU. Sennhauser
AbstractFailures have to be avoided by proper design, material selection and manufacturing. Properties, degradation mechanisms, and expected lifetime of materials are introduced and the basics of failure analysis and analysis equipment are presented. Failures will be demonstrated experimentally and the opportunity is offered to perform a failure analysis with advanced equipment in the laboratory.
ObjectiveIntroduction to the degradation and failure mechanisms and causes of electronic components, devices and systems as well as to methods and tools of reliability testing, characterization and failure analysis.
ContentSummary of reliability and failure analysis terminology; physics of failure: materials properties, physical processes and failure mechanisms; failure analysis of ICs, PCBs, opto-electronics, discrete and other components and devices; basics and properties of instruments; application in circuit design and reliability analysis
Lecture notesComprehensive copy of transparencies
Energy and Power Electronics
Core Subjects
These core subjects are particularly recommended for the field of "Energy and Power Electronics".
NumberTitleTypeECTSHoursLecturers
227-0526-00LPower System Analysis Information W6 credits4GG. Hug
AbstractThe goal of this course is understanding the stationary and dynamic problems in electrical power systems. The course includes the development of stationary models of the electrical network, their mathematical representation and special characteristics and solution methods of large linear and non-linear systems of equations related to electrical power networks.
ObjectiveThe goal of this course is understanding the stationary and dynamic problems in electrical power systems and the application of analysis tools in steady and dynamic states.
ContentThe course includes the development of stationary models of the electrical network, their mathematical representation and special characteristics and solution methods of large linear and non-linear systems of equations related to electrical power grids. Approaches such as the Newton-Raphson algorithm applied to power flow equations, superposition technique for short-circuit analysis, equal area criterion and nose curve analysis are discussed as well as power flow computation techniques for distribution grids.
Lecture notesLecture notes.
Systems and Control
Recommended Subjects
These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
227-0526-00LPower System Analysis Information W6 credits4GG. Hug
AbstractThe goal of this course is understanding the stationary and dynamic problems in electrical power systems. The course includes the development of stationary models of the electrical network, their mathematical representation and special characteristics and solution methods of large linear and non-linear systems of equations related to electrical power networks.
ObjectiveThe goal of this course is understanding the stationary and dynamic problems in electrical power systems and the application of analysis tools in steady and dynamic states.
ContentThe course includes the development of stationary models of the electrical network, their mathematical representation and special characteristics and solution methods of large linear and non-linear systems of equations related to electrical power grids. Approaches such as the Newton-Raphson algorithm applied to power flow equations, superposition technique for short-circuit analysis, equal area criterion and nose curve analysis are discussed as well as power flow computation techniques for distribution grids.
Lecture notesLecture notes.
Signal Processing and Machine Learning
Coming soon!
Core Subjects
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Subjects of General Interest
NumberTitleTypeECTSHoursLecturers
227-0377-00LPhysics of Failure and Failure Analysis of Electronic Devices and EquipmentW3 credits2VU. Sennhauser
AbstractFailures have to be avoided by proper design, material selection and manufacturing. Properties, degradation mechanisms, and expected lifetime of materials are introduced and the basics of failure analysis and analysis equipment are presented. Failures will be demonstrated experimentally and the opportunity is offered to perform a failure analysis with advanced equipment in the laboratory.
ObjectiveIntroduction to the degradation and failure mechanisms and causes of electronic components, devices and systems as well as to methods and tools of reliability testing, characterization and failure analysis.
ContentSummary of reliability and failure analysis terminology; physics of failure: materials properties, physical processes and failure mechanisms; failure analysis of ICs, PCBs, opto-electronics, discrete and other components and devices; basics and properties of instruments; application in circuit design and reliability analysis
Lecture notesComprehensive copy of transparencies
Energy Science and Technology Master Information
Core Subjects
Compulsory core courses
NumberTitleTypeECTSHoursLecturers
227-1631-00LEnergy System Analysis Information W4 credits3GG. Hug, S. Hellweg, F. Noembrini, A. Schlüter
AbstractThe course provides an introduction to the methods and tools for analysis of energy consumption, energy production and energy flows. Environmental aspects are included as well as economical considerations. Different sectors of the society are discussed, such as electric power, buildings, and transportation. Models for energy system analysis planning are introduced.
ObjectiveThe purpose of the course is to give the participants an overview of the methods and tools used for energy systems analysis and how to use these in simple practical examples.
ContentThe course gives an introduction to methods and tools for analysis of energy consumption, energy production and energy flows. Both larger systems, e.g. countries, and smaller systems, e.g. industries, homes, vehicles, are studied. The tools and methods are applied to various problems during the exercises. Different conventions of energy statistics used are introduced.

The course provides also an introduction to energy systems models for developing scenarios of future energy consumption and production. Bottom-up and Top-Down approaches are addressed and their features and applications discussed.

The course contains the following parts:
Part I: Energy flows and energy statistics
Part II: Environmental impacts
Part III: Electric power systems
Part IV: Energy in buildings
Part V: Energy in transportation
Part VI: Energy systems models
Lecture notesHandouts
LiteratureExcerpts from various books, e.g. K. Blok: Introduction to Energy Analysis, Techne Press, Amsterdam 2006, ISBN 90-8594-016-8
Elective Core Courses
These courses are particularly recommended, other ETH-courses from the field of Energy Science and Technology at large may be chosen in accordance with your tutor.
NumberTitleTypeECTSHoursLecturers
227-0526-00LPower System Analysis Information W6 credits4GG. Hug
AbstractThe goal of this course is understanding the stationary and dynamic problems in electrical power systems. The course includes the development of stationary models of the electrical network, their mathematical representation and special characteristics and solution methods of large linear and non-linear systems of equations related to electrical power networks.
ObjectiveThe goal of this course is understanding the stationary and dynamic problems in electrical power systems and the application of analysis tools in steady and dynamic states.
ContentThe course includes the development of stationary models of the electrical network, their mathematical representation and special characteristics and solution methods of large linear and non-linear systems of equations related to electrical power grids. Approaches such as the Newton-Raphson algorithm applied to power flow equations, superposition technique for short-circuit analysis, equal area criterion and nose curve analysis are discussed as well as power flow computation techniques for distribution grids.
Lecture notesLecture notes.
Other Elective Courses
NumberTitleTypeECTSHoursLecturers
151-0360-00LProcedures for the Analysis of StructuresW4 credits2V + 1UG. Kress
AbstractBasic theories for structure integrity calculations are presented with focus on strength, stability, fatigue and elasto-plastic structural analysis.
Theories and models for one dimesional and planar structures are presented based on energy theorems.
ObjectiveBasic principles applied in structural mechanics. Introduction to the theories of planar structures. Development of an understanding of the relationship between material properties, structural theories and design criteria.
Content1. Basic problem of continuum mechanics and energy principles: structural theories, homogenization theories; finite elements; fracture mechanics.
2.Structural theories for planar structures and stability: plane-stress, plate theory, buckling of plates (non-linear plate theory).
3.Strength of material theories and material properties: ductile behaviour, plasticity, von Mises, Tresca, principal stress criterion; brittle behaviour; viscoplastic behaviour, creep resistance.
4. Structural design: fatigue and dynamic structural analysis.
Lecture notesScript and all other course material available on MOODLE
Prerequisites / Noticenone
Earth Sciences Bachelor Information
Bachelor Studies (Programme Regulations 2016)
1. Semester
First Year Examinations
NumberTitleTypeECTSHoursLecturers
401-0251-00LMathematics IO6 credits4V + 2UL. Halbeisen
AbstractThis course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.
ObjectiveMathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment.

The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses.
Content1. Single-Variable Calculus:
review of differentiation, linearisation, Taylor polynomials, maxima and minima, antiderivative, fundamental theorem of calculus, integration methods, improper integrals.

2. Linear Algebra and Complex Numbers:
systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra.

3. Ordinary Differential Equations:
separable ordinary differential equations (ODEs), integration by substitution, 1st and 2nd order linear ODEs, homogeneous systems of linear ODEs with constant coefficients, introduction to 2-dimensional dynamical systems.
Literature- Thomas, G. B.: Thomas' Calculus, Part 1 (Pearson Addison-Wesley).
- Bretscher, O.: Linear Algebra with Applications (Pearson Prentice Hall).
Prerequisites / NoticePrerequisites: familiarity with the basic notions from Calculus, in particular those of function and derivative.

Mathe-Lab (Assistance):
Mondays 12-14, Tuesdays 17-19, Wednesdays 17-19, in Room HG E 41.
General Courses in Earth Sciences
NumberTitleTypeECTSHoursLecturers
651-4271-00LData Analysis and Visualisation with Matlab in Earth SciencesO3 credits3GS. Wiemer, G. De Souza, T. Tormann
AbstractThis lecture and the corresponding exercises provide the students with an introduction to the concepts and tools of scientific data analysis. Based on current questions in the Earth Sciences, the students solve problems of increasing complexity both in small groups and singly using the software package MATLAB. Students also learn how to effectively visualise different kinds of datasets.
ObjectiveThe following concepts are introduced in the course:
- Effective data analysis and visualisation in 2D and 3D
- Working with matrices and arrays
- Programming and development of algorithms
- Learning to effectively use animations
- Statistical description of a dataset
- Interactive data-mining
- Uncertainty, error propagation and bootstrapping
- Regression analysis
- Testing hypotheses
3. Semester
Basic Courses II
Examination Block 2
NumberTitleTypeECTSHoursLecturers
701-0071-00LMathematics III: Systems AnalysisO4 credits2V + 1UN. Gruber, M. Vogt
AbstractThe objective of the systems analysis course is to deepen and illustrate the mathematical concepts on the basis of a series of very concrete examples. Topics covered include: linear box models with one or several variables, non-linear box models with one or several variables, time-discrete models, and continuous models in time and space.
ObjectiveLearning and applying of concepts (models) and quantitative methods to address concrete problems of environmental relevance. Understanding and applying the systems-analytic approach, i.e., Recognizing the core of the problem - simplification - quantitative approach - prediction.
ContentLink
Lecture notesOverhead slides will be made available through Ilias.
LiteratureImboden, D.S. and S. Pfenninger (2013) Introduction to Systems Analysis: Mathematically Modeling Natural Systems. Berlin Heidelberg: Springer Verlag.

Link
Bachelor Studies (Programme Regulations 2010)
5. Semester Majors
Major in Climate and Water: Electives
Advisor of the BSc-major "Climate and Water" is Dr. Erich Fischer, Institute for climate and atmosphere (IAC).
Major in Climate and Water: Electives
In addition to the mandatory seminar for Bachelor Students: Atmosphere and Climate (course nr. 701-0459-00 in autumn semester) another 22 credits must be acquired from the offered elective courses during the 5th and 6th semester. The choice of other courses has to be granted by the advisor (Dr. Erich Fischer).
NumberTitleTypeECTSHoursLecturers
401-6215-00LUsing R for Data Analysis and Graphics (Part I) Information W1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the first part an introduction to the statistical software R for scientists. Topics covered are data generation and selection, graphical and basic statistical functions, creating simple functions, basic types of objects.
ObjectiveThe students will be able to use the software R for simple data analysis.
ContentThe course provides the first part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part I of the course covers the following topics:
- What is R?
- R Basics: reading and writing data from/to files, creating vectors & matrices, selecting elements of dataframes, vectors and matrices, arithmetics;
- Types of data: numeric, character, logical and categorical data, missing values;
- Simple (statistical) functions: summary, mean, var, etc., simple statistical tests;
- Writing simple functions;
- Introduction to graphics: scatter-, boxplots and other high-level plotting functions, embellishing plots by title, axis labels, etc., adding elements (lines, points) to existing plots.

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link

Note: Part I of UsingR is complemented and extended by Part II, which is offered during the second part of the semester and which can be taken independently from Part I.
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeThe course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
Earth Sciences Master Information
Major in Geology
Compulsory Module in Analytical Methods in Earth Sciences
Students have to complete 6 credits in part A, and 6 credits in part B.
Part B: Methods
NumberTitleTypeECTSHoursLecturers
651-4117-00LSediment AnalysisW+3 credits2GM. G. Fellin, A. Gilli, V. Picotti
AbstractTheoretical background and application of some basic methods for sediment analysis.
ObjectiveThe main goal is to learn how to apply the analysis of the texture and grain-size of sediments to constrain the sedimentary processes and environments.
ContentA one-day fieldtrip to a local outcrop to learn how to describe sediments in the field and to collect samples for grain-size and compositional analysis. Application of the same analytical techniques on samples of unknown origin: the sampling sites will be revealed at the end of the course. Discussion of the theoretical background and of the results in class. At the end of the course, the student will have to hand in a report with the presentation and discussion of all the data produced during the course.
Lecture notesFor the various analytical methods English texts will be provided in class.
LiteratureIntroduction to clastic sedimentology. R.J. Cheel
Open Choice Modules Geology
Basin Analysis
Basin Analysis: Compulsory Courses
NumberTitleTypeECTSHoursLecturers
651-4231-00LBasin AnalysisW+3 credits2GS. Willett, T. I. Eglinton, M. Lupker
AbstractThe course discusses the formation and development of different basin types as part of lithosphere geodynamics. It introduces conceptual models and governing physics, with practical application to the study of basin evolution. Techniques for the analysis of subsidence and thermal history are demonstrated. Organic matter, petroleum play, and their biogeochemical investigation are examined.
ObjectiveBased on the introductory education and practical training during this course, each participant should be able to choose and apply approaches and techniques to own problems of basin analysis, and should be versed to expand their knowledge independently.

In particular, each participant should:

- Develop an intuitive understanding for origin, dynamics, and temporal evolution of basins in a geological / geodynamic context;

- Acquire the necessary theoretical foundation to describe basin evolution quantitatively;

- Be familiar with geological and geophysical methods that are applied to obtain information about rock properties, structural geometry, and thermal and subsidence history of basins;

- Understand the burial and maturation of organic matter in basins, the development of petroleum play, and be acquainted with geochemical methods to study the evolution of biogenic carbon.
ContentThe following topics are covered:

- Introduction; classification schemes and types of basins; heat conduction; geotherms;

- The lithosphere; isostasy; rifts and basins due to lithospheric stretching; uniform extension model; modifications to the uniform stretching model; dynamics of rifting.

- Elasticity of the lithosphere; flexural compensation; geometry and analytical description of loads and the resulting deflection; foreland basins; their anatomy;

- Reconstruction of basin evolution; borehole data; porosity loss and decompaction; backstripping; subsidence curves; thermal history and its reconstruction;

- Petroleum play concept; organic production; source rock prediction and depositional environment; petroleum generation, expulsion, migration, alteration; reservoir and traps;

- Carbon cycle; maturation of organic matter; geochemistry of biogenic carbon; biomarkers; analytical techniques

- Overview of other basin types: effects of mantle dynamics, strike-slip basins.

Each week of the course is split in lectures and corresponding practicals, in which the concepts are applied to simplified problems.

Grading of the semester performance is based on submitted practicals (50%) and a final exam (50%). The exam will take place in the time slot of the last practical (18.12.).
Lecture notesLecture notes are provided online during the course. They summarize the current subjects week by week, and provide the essential theoretical background.
LiteratureMain reference :

Allen, P.A., and Allen, J.R., 2013. Basin Analysis - Principles and Application to petroleum play assessment
3rd edition, 619 pp. Wiley-Blackwell, Chichester, UK.
ISBN 978-0-470-67376-8

Recommended, but not required (available in library).



Supplementary:
Turcotte, D.L., and Schubert, S., 2002. Geodynamics.
2nd edition, 456 pp. Cambridge University Press.
ISBN 0-521-66624-4.

Peters, K.E., Walters, C.C., Moldowan, J.M., 2005. The biomarker guide (volume 2).
2nd edition, Cambridge University Press.
ISBN 0-521-83762-6.
Prerequisites / NoticeFamiliarity with MATLAB is advantageous, but not required.
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
406-0243-AALAnalysis I and II Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-14 credits30RM. Akka Ginosar
AbstractMathematical tools for the engineer
ObjectiveMathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers.
ContentComplex numbers.
Calculus for functions of one variable with applications.
Simple Mathematical models in engineering.

Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion, Lagrange multipliers. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. Ordinary differential equations.
LiteratureTextbooks in English:
- J. Stewart: Calculus, Cengage Learning, 2009, ISBN 978-0-538-73365-6.
- J. Stewart: Multivariable Calculus, Thomson Brooks/Cole.
- V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus.
- W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education. ISBN 978-0-321-65193-8.
Textbooks in German:
- M. Akveld, R. Sperb: Analysis I, vdf
- M. Akveld, R. Sperb: Analysis II, vdf
- L. Papula: Mathematik für Ingenieure und Naturwissenschaftler, Vieweg Verlag
- L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag
Geomatic Engineering and Planning Bachelor Information
1. Semester
First Year Examinations
NumberTitleTypeECTSHoursLecturers
401-0241-00LAnalysis I Information O7 credits5V + 2UM. Akka Ginosar
AbstractMathematical tools for the engineer
ObjectiveMathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers.
ContentComplex numbers.
Calculus for functions of one variable with applications.
Simple Mathematical models in engineering.
Lecture notesDie Vorlesung folgt weitgehend

Klaus Dürrschnabel, "Mathematik für Ingenieure - Eine Einführung mit Anwendungs- und Alltagsbeispielen", Springer; online verfügbar unter:
Link
LiteratureNeben Klaus Dürrschnabel, "Mathematik für Ingenieure - Eine Einführung mit Anwendungs- und Alltagsbeispielen", Springer sind auch die folgenden Bücher/Skripte empfehlenswert und decken den zu behandelnden Stoff ab:

Tilo Arens et al., "Mathematik", Springer; online verfügbar unter:
Link

Meike Akveld, "Analysis 1", vdf;
Link

Urs Stammbach, "Analysis I/II" (erhältlich im ETH Store);
Link
Geomatic Engineering Master Information
Electives
The entire course programs of ETH Zurich and the University of Zurich are open to the students to individual selection.
Recommended Electives of Master Degree Programme
NumberTitleTypeECTSHoursLecturers
101-0439-00LIntroduction to Economic Analysis - A Case Study Approach with Cost Benefit Analysis in Transport
Remark:
Former Title "Introduction to Economic Policy - A Case Study Approach with Cost Benefit Analysis in Transport".
W6 credits4GK. W. Axhausen, R. Schubert
AbstractThe course presents basic economic principles as well as cost benefit analyses in transport; it also introduces methods used to derive the monetary values of non-market goods.
ObjectiveFamiliarity with basic microeconomic and macroeconomic principles and with the essential methods of project appraisal
ContentBasic microeconomic and macroeconomic üpronciples; Cost-Benefit-Analyses; multi-criteria analyses; European guidelines; stated response methods; travel cost approach and others; Valuation of travel time savings; valuation of traffic safety
Lecture notesmoodle platform for the basic economic principles; handouts
LiteratureTaylor, M.P., Mankiw, N.G. (2014): Economics; Harvard Press

VSS (2006) SN 640 820: Kosten-Nutzen-Analysen im Strassenverkehr, VSS, Zürich.

Boardman, A.E., D.H. Greenberg, A.R. Vining und D.L. Weimer (2001) Cost – Benefit – Analysis: Concepts and Practise, Prentice-Hall, Upper Saddle River.

ecoplan and metron (2005) Kosten-Nutzen-Analysen im Strassenverkehr: Kommentar zu SN 640 820, UVEK, Bern.
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
103-0255-AALGeodata Analysis
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-2 credits4RM. Raubal
AbstractThe course deals with advanced methods in spatial data analysis.
Objective- Understanding the theoretical principles in spatial data analysis.
- Understanding and using methods for spatial data analysis.
- Detecting common sources of errors in spatial data analysis.
- Advanced practical knowledge in using appropriate GIS-tools.
ContentThe course deals with advanced methods in spatial data analysis in theory as well as in practical exercises.
LiteratureMITCHELL, A., 2012, The Esri Guide to GIS Analysis - Modeling Suitability, Movement, and Interaction (3. Auflage), ESRI Press, Redlands, California
406-0242-AALAnalysis II Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-7 credits15RM. Akka Ginosar
AbstractMathematical tools of an engineer
ObjectiveMathematics as a tool to solve engineering problems, mathematical formulation of problems in science and engineering. Basic mathematical knowledge of an engineers.
ContentMulti variable calculus: gradient, directional derivative, chain rule, Taylor expansion, Lagrange multipliers. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. Ordinary differential equations.
LiteratureTextbooks in English:
- J. Stewart: Multivariable Calculus, Thomson Brooks/Cole
- V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus
- W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education

- M. Akveld, R. Sperb, Analysis II, vdf
- L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag
406-0243-AALAnalysis I and II Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-14 credits30RM. Akka Ginosar
AbstractMathematical tools for the engineer
ObjectiveMathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers.
ContentComplex numbers.
Calculus for functions of one variable with applications.
Simple Mathematical models in engineering.

Multi variable calculus: gradient, directional derivative, chain rule, Taylor expansion, Lagrange multipliers. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. Ordinary differential equations.
LiteratureTextbooks in English:
- J. Stewart: Calculus, Cengage Learning, 2009, ISBN 978-0-538-73365-6.
- J. Stewart: Multivariable Calculus, Thomson Brooks/Cole.
- V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus.
- W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education. ISBN 978-0-321-65193-8.
Textbooks in German:
- M. Akveld, R. Sperb: Analysis I, vdf
- M. Akveld, R. Sperb: Analysis II, vdf
- L. Papula: Mathematik für Ingenieure und Naturwissenschaftler, Vieweg Verlag
- L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag
Health Sciences and Technology Bachelor Information
Electives
NumberTitleTypeECTSHoursLecturers
551-1003-00LMethods of Biological Analysis Information W3 credits3GR. Aebersold, M. Badertscher, K. Weis
Abstract529-1042-00
Principles of the most important separation techniques and the interpretation of molecular spectra.

551-1003-00
The course will teach the basis and typical applications of methods for the analysis of nucleic acid sequences, mass spectrometric analysis of proteins and proteomes and advanced light and fluorescent imaging methods.
Objective529-1042-00
Knowledge of the necessary basics and the possibilities of application of the relevant spectroscopical and separation methods in analytical chermistry.

551-1003-00
Knowledge of the theoretical basis of the methods for nucleic acid sequence analysis, mass spectrometry based protein and proteome analysis and advanced light and fluorescent imaging methods, and an understanding of the application of these principles in experimental biology.
Content529-1042-00
Application oriented basics of instrumental analysis in organic chemistry and the empirical employment of the methods of structure elucidation (mass spectrometry, NMR-, IR-, UV/VIS spectroscopy). Basics and application of chromatographic and electrophoretic separation methods. Application of the knowledge by practising.

551-1003-00
The course will consist of lectures covering the theoretical and technical base of the respective analytical methods and of exercises where typical applications of the methods in modern experimental biology are discussed.
Lecture notes529-1042-00
A comprehensive script is available in the HCI-Shop. A summary of the part "Spektroskopie" defines the relevant material for the exam.

551-1003-00
Materials supporting the lectures and exercises will be made available via Moodle.
Literature529-1042-00
- Pretsch E., Bühlmann P., Badertscher M. Structure Determination of Organic Compounds, 5th revised and enlarged English edition, Springer-Verlag, Berlin 2009;
- Pretsch E., Bühlmann P., Badertscher M., Spektroskopische Daten zur Strukturaufklärung organischer Verbindungen, fünfte Auflage, Springer-Verlag, Berlin 2010;
- D.A. Skoog, J.J. Leary, Instrumentelle Analytik, Grundlagen, Geräte, Anwendungen, Springer, Berlin, 1996;
- K. Cammann, Instrumentelle Analytische Chemie, Verfahren, Anwendungen, Qualitätssicherung, Spektrum Akademischer Verlag, Heidelberg, 2001;
- R. Kellner, J.-M. Mermet, M. Otto, H.M. Widmer, Analytical Chemistry, Wiley-VCH Verlag, Weinheim, 1998;
- K. Robards, P.R.Haddad, P.E. Jackson, Principles and practice of modern chromatographic methods, Academic Press, London, 1994;
Prerequisites / Notice529-1042-00
Prerequisites:
- 529-1001-01 V "Allgemeine Chemie I (für Biol./Pharm.Wiss.)"
- 529-1001-00 P "Allgemeine Chemie I (für Biol./Pharm.Wiss.)"
- 529-1011-00 G "Organische Chemie I (für Biol./Pharm.Wiss.)"
Health Sciences and Technology Master Information
Major in Human Movement Science and Sport
Electives
Elective Courses II
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
376-2019-00LApplied Movement Analysis Information W2 credits2GR. Scharpf, S. Lorenzetti
AbstractBased on practical examples out of sport, everyday movement and therapy, students use and compare different methods of movement analysis.
ObjectiveStudents are able to assess human movement using different methods of movement analysis.
ContentDuring the course students get acquainted with different methods of movement analysis such as: functional, morphological, clinical, mechanical, and others.
Based on practical examples, these methods are used and compared. The examples range from sport, everyday movement and therapy, such as hockey, gymnastics, acrobatics, badminton, gait / running and strength training. In the first phase of the class, the different approaches are applied. In the second phase, small teams are working on individual projects. These will be discussed and presented in plenum.
Lecture notesClass material will be distributed using the moodle platform.
Major in Medical Technology
Electives
Elective Courses II
NumberTitleTypeECTSHoursLecturers
227-0391-00LMedical Image Analysis
Does not take place this semester.
W3 credits2GE. Konukoglu
AbstractIt is the objective of this lecture to introduce the basic concepts used
in Medical Image Analysis. In particular the lecture focuses on shape
representation schemes, segmentation techniques, and the various image registration methods commonly used in Medical Image Analysis applications.
ObjectiveThis lecture aims to give an overview of the basic concepts of Medical Image Analysis and its application areas.
Prerequisites / NoticeBasic knowledge of computer vision would be helpful.
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
227-0969-00LMethods & Models for fMRI Data Analysis Information W6 credits4VK. Stephan
AbstractThis course teaches methods and models for fMRI data analysis, covering all aspects of statistical parametric mapping (SPM), incl. preprocessing, the general linear model, statistical inference, multiple comparison corrections, event-related designs, and Dynamic Causal Modelling (DCM), a Bayesian framework for identification of nonlinear neuronal systems from neurophysiological data.
ObjectiveTo obtain in-depth knowledge of the theoretical foundations of SPM
and DCM and of their application to empirical fMRI data.
ContentThis course teaches state-of-the-art methods and models for fMRI data analysis. It covers all aspects of statistical parametric mapping (SPM), incl. preprocessing, the general linear model, frequentist and Bayesian inference, multiple comparison corrections, and event-related designs, and Dynamic Causal Modelling (DCM), a Bayesian framework for identification of nonlinear neuronal systems from neurophysiological data. A particular emphasis of the course will be on methodological questions arising in the context of studies in psychiatry, neurology and neuroeconomics.
Major in Molecular Health Sciences
Electives
Elective Courses II
NumberTitleTypeECTSHoursLecturers
551-1003-00LMethods of Biological Analysis Information W3 credits3GR. Aebersold, M. Badertscher, K. Weis
Abstract529-1042-00
Principles of the most important separation techniques and the interpretation of molecular spectra.

551-1003-00
The course will teach the basis and typical applications of methods for the analysis of nucleic acid sequences, mass spectrometric analysis of proteins and proteomes and advanced light and fluorescent imaging methods.
Objective529-1042-00
Knowledge of the necessary basics and the possibilities of application of the relevant spectroscopical and separation methods in analytical chermistry.

551-1003-00
Knowledge of the theoretical basis of the methods for nucleic acid sequence analysis, mass spectrometry based protein and proteome analysis and advanced light and fluorescent imaging methods, and an understanding of the application of these principles in experimental biology.
Content529-1042-00
Application oriented basics of instrumental analysis in organic chemistry and the empirical employment of the methods of structure elucidation (mass spectrometry, NMR-, IR-, UV/VIS spectroscopy). Basics and application of chromatographic and electrophoretic separation methods. Application of the knowledge by practising.

551-1003-00
The course will consist of lectures covering the theoretical and technical base of the respective analytical methods and of exercises where typical applications of the methods in modern experimental biology are discussed.
Lecture notes529-1042-00
A comprehensive script is available in the HCI-Shop. A summary of the part "Spektroskopie" defines the relevant material for the exam.

551-1003-00
Materials supporting the lectures and exercises will be made available via Moodle.
Literature529-1042-00
- Pretsch E., Bühlmann P., Badertscher M. Structure Determination of Organic Compounds, 5th revised and enlarged English edition, Springer-Verlag, Berlin 2009;
- Pretsch E., Bühlmann P., Badertscher M., Spektroskopische Daten zur Strukturaufklärung organischer Verbindungen, fünfte Auflage, Springer-Verlag, Berlin 2010;
- D.A. Skoog, J.J. Leary, Instrumentelle Analytik, Grundlagen, Geräte, Anwendungen, Springer, Berlin, 1996;
- K. Cammann, Instrumentelle Analytische Chemie, Verfahren, Anwendungen, Qualitätssicherung, Spektrum Akademischer Verlag, Heidelberg, 2001;
- R. Kellner, J.-M. Mermet, M. Otto, H.M. Widmer, Analytical Chemistry, Wiley-VCH Verlag, Weinheim, 1998;
- K. Robards, P.R.Haddad, P.E. Jackson, Principles and practice of modern chromatographic methods, Academic Press, London, 1994;
Prerequisites / Notice529-1042-00
Prerequisites:
- 529-1001-01 V "Allgemeine Chemie I (für Biol./Pharm.Wiss.)"
- 529-1001-00 P "Allgemeine Chemie I (für Biol./Pharm.Wiss.)"
- 529-1011-00 G "Organische Chemie I (für Biol./Pharm.Wiss.)"
Major in Neurosciences
Electives
Elective Courses II
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
High-Energy Physics (Joint Master with EP Paris) Information
Electives
Optional Subjects in Mathematics
NumberTitleTypeECTSHoursLecturers
401-3461-00LFunctional Analysis I Information
At most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics.
W10 credits4V + 1UA. Carlotto
AbstractBaire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications.
ObjectiveAcquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
Lecture notesLecture Notes on "Funktionalanalysis I" by Michael Struwe
LiteratureA primary reference for the course is the textbook by H. Brezis:

Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

Other useful, and recommended references are the following:

Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
Prerequisites / NoticeSolid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces).
Computer Science Bachelor Information
Bachelor Studies (Programme Regulations 2016)
Basic Courses
NumberTitleTypeECTSHoursLecturers
401-0213-16LAnalysis II Information O5 credits2V + 2UÖ. Imamoglu
AbstractDifferential and Integral calculus in many variables, vector analysis.
ObjectiveDifferential and Integral calculus in many variables, vector analysis.
ContentDifferential and Integral calculus in many variables, vector analysis.
LiteratureFür allgemeine Informationen, sehen Sie bitte die Webseite der Vorlesung: Link
Minor Courses
NumberTitleTypeECTSHoursLecturers
651-4271-00LData Analysis and Visualisation with Matlab in Earth SciencesW3 credits3GS. Wiemer, G. De Souza, T. Tormann
AbstractThis lecture and the corresponding exercises provide the students with an introduction to the concepts and tools of scientific data analysis. Based on current questions in the Earth Sciences, the students solve problems of increasing complexity both in small groups and singly using the software package MATLAB. Students also learn how to effectively visualise different kinds of datasets.
ObjectiveThe following concepts are introduced in the course:
- Effective data analysis and visualisation in 2D and 3D
- Working with matrices and arrays
- Programming and development of algorithms
- Learning to effectively use animations
- Statistical description of a dataset
- Interactive data-mining
- Uncertainty, error propagation and bootstrapping
- Regression analysis
- Testing hypotheses
Integrated Building Systems Master Information
Main Courses
Specialised Courses
NumberTitleTypeECTSHoursLecturers
101-0187-00LStructural Reliability and Risk Analysis Information W3 credits2GS. Marelli
AbstractStructural reliability aims at quantifying the probability of failure of systems due to uncertainties in their design, manufacturing and environmental conditions. Risk analysis combines this information with the consequences of failure in view of optimal decision making. The course presents the underlying probabilistic modelling and computational methods for reliability and risk assessment.
ObjectiveThe goal of this course is to provide the students with a thorough understanding of the key concepts behind structural reliability and risk analysis. After this course the students will have refreshed their knowledge of probability theory and statistics to model uncertainties in view of engineering applications. They will be able to analyze the reliability of a structure and to use risk assessment methods for decision making under uncertain conditions. They will be aware of the state-of-the-art computational methods and software in this field.
ContentEngineers are confronted every day to decision making under limited amount of information and uncertain conditions. When designing new structures and systems, the design codes such as SIA or Euro- codes usually provide a framework that guarantees safety and reliability. However the level of safety is not quantified explicitly, which does not allow the analyst to properly choose between design variants and evaluate a total cost in case of failure. In contrast, the framework of risk analysis allows one to incorporate the uncertainty in decision making.

The first part of the course is a reminder on probability theory that is used as a main tool for reliability and risk analysis. Classical concepts such as random variables and vectors, dependence and correlation are recalled. Basic statistical inference methods used for building a probabilistic model from the available data, e.g. the maximum likelihood method, are presented.

The second part is related to structural reliability analysis, i.e. methods that allow one to compute probabilities of failure of a given system with respect to prescribed criteria. The framework of reliability analysis is first set up. Reliability indices are introduced together with the first order-second moment method (FOSM) and the first order reliability method (FORM). Methods based on Monte Carlo simulation are then reviewed and illustrated through various examples. By-products of reliability analysis such as sensitivity measures and partial safety coefficients are derived and their links to structural design codes is shown. The reliability of structural systems is also introduced as well as the methods used to reassess existing structures based on new information.

The third part of the course addresses risk assessment methods. Techniques for the identification of hazard scenarios and their representation by fault trees and event trees are described. Risk is defined with respect to the concept of expected utility in the framework of decision making. Elements of Bayesian decision making, i.e. pre-, post and pre-post risk assessment methods are presented.

The course also includes a tutorial using the UQLab software dedicated to real world structural reliability analysis.
Lecture notesSlides of the lectures are available online every week. A printed version of the full set of slides is proposed to the students at the beginning of the semester.
LiteratureAng, A. and Tang, W.H, Probability Concepts in Engineering - Emphasis on Applications to Civil and Environmental Engineering, 2nd Edition, John Wiley & Sons, 2007.

S. Marelli, R. Schöbi, B. Sudret, UQLab user manual - Structural reliability (rare events estimation), Report UQLab-V0.92-107.
Prerequisites / NoticeBasic course on probability theory and statistics
Interdisciplinary Sciences Bachelor Information
Physical-Chemical Direction
1. Semester (Physical-Chemical Direction)
Compulsory Subjects First Year Examinations
NumberTitleTypeECTSHoursLecturers
401-1261-07LAnalysis I Information O10 credits6V + 3UM. Einsiedler
AbstractIntroduction to the differential and integral calculus in one real variable: fundaments of mathematical thinking, numbers, sequences, basic point set topology, continuity, differentiable functions, ordinary differential equations, Riemann integration.
ObjectiveThe ability to work with the basics of calculus in a mathematically rigorous way.
LiteratureH. Amann, J. Escher: Analysis I
Link

J. Appell: Analysis in Beispielen und Gegenbeispielen
Link

R. Courant: Vorlesungen über Differential- und Integralrechnung
Link

O. Forster: Analysis 1
Link

H. Heuser: Lehrbuch der Analysis
Link

K. Königsberger: Analysis 1
Link

W. Walter: Analysis 1
Link

V. Zorich: Mathematical Analysis I (englisch)
Link

A. Beutelspacher: "Das ist o.B.d.A. trivial"
Link

H. Schichl, R. Steinbauer: Einführung in das mathematische Arbeiten
Link
3. Semester (Physical-Chemical Direction)
Electives
For the Bachelor in Interdisciplinary Sciences students can in principle choose from all subjects taught at the Bachelor level at ETH Zurich.



At the beginning of the 2. year an individual study programme is established for every student in discussion with the Director of Studies in interdisciplinary sciences. For details see Programme Regulations 2010.
NumberTitleTypeECTSHoursLecturers
401-2303-00LComplex Analysis Information W6 credits3V + 2UR. Pandharipande
AbstractComplex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, special functions, conformal mappings, Riemann mapping theorem.
ObjectiveWorking Knowledge with functions of one complex variables; in particular applications of the residue theorem
LiteratureTh. Gamelin: Complex Analysis. Springer 2001

E. Titchmarsh: The Theory of Functions. Oxford University Press

D. Salamon: "Funktionentheorie". Birkhauser, 2011. (In German)

L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co.

B. Palka: "An introduction to complex function theory."
Undergraduate Texts in Mathematics. Springer-Verlag, 1991.

R.Remmert: Theory of Complex Functions. Springer Verlag
Biochemical-Physical Direction
1. Semester (Biochemical-Physical Direction)
Compulsory Subjects First Year Examinations
NumberTitleTypeECTSHoursLecturers
401-0271-00LMathematical Foundations I: Analysis AW5 credits3V + 2UL. Kobel-Keller
AbstractIntroduction to calculus in one dimension. Building simple models and analysing them mathematically.
Functions of one variable: the notion of a function, of the derivative, the idea of a differential equation, complex numbers, Taylor polynomials and Taylor series. The integral of a function of one variable.
ObjectiveIntroduction to calculus in one dimension. Building simple models and analysing them mathematically.
ContentFunctions of one variable: the notion of a function, of the derivative, the idea of a differential equation, complex numbers, Taylor polynomials and Taylor series. The integral of a function of one variable.
LiteratureG. B. Thomas, M. D. Weir, J. Hass: Analysis 1, Lehr- und Übungsbuch, Pearson-Verlag
D. W. Jordan, P. Smith: Mathematische Methoden für die Praxis, Spektrum Akademischer Verlag
R. Sperb/M. Akveld: Analysis I (vdf)
L. Papula: Mathematik für Ingenieure und Naturwissenschaftler (3 Bände), Vieweg
further reading suggestions will be indicated during the lecture
401-1261-07LAnalysis I Information W10 credits6V + 3UM. Einsiedler
AbstractIntroduction to the differential and integral calculus in one real variable: fundaments of mathematical thinking, numbers, sequences, basic point set topology, continuity, differentiable functions, ordinary differential equations, Riemann integration.
ObjectiveThe ability to work with the basics of calculus in a mathematically rigorous way.
LiteratureH. Amann, J. Escher: Analysis I
Link

J. Appell: Analysis in Beispielen und Gegenbeispielen
Link

R. Courant: Vorlesungen über Differential- und Integralrechnung
Link

O. Forster: Analysis 1
Link

H. Heuser: Lehrbuch der Analysis
Link

K. Königsberger: Analysis 1
Link

W. Walter: Analysis 1
Link

V. Zorich: Mathematical Analysis I (englisch)
Link

A. Beutelspacher: "Das ist o.B.d.A. trivial"
Link

H. Schichl, R. Steinbauer: Einführung in das mathematische Arbeiten
Link
401-0231-10LAnalysis IW8 credits4V + 3UT. H. Willwacher
AbstractCalculus of one variable: Real and complex numbers, vectors, limits, sequences, series, power series, continuous maps, differentiation and integration in one variable, introduction to ordinary differential equations
ObjectiveEinfuehrung in die Grundlagen der Analysis
Lecture notesKonrad Koenigsberger, Analysis I.
Christian Blatter: Ingenieur-Analysis (Kapitel 1-3)
3. Semester (Biochemical-Physical Direction)
Compulsory Subjects Examination Block
NumberTitleTypeECTSHoursLecturers
401-0353-00LAnalysis III Information W4 credits2V + 1UA. Figalli
AbstractIn this lecture we treat problems in applied analysis. The focus lies on the simplest cases of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation and the wave equation.
Objective
Content1.) Klassifizierung von PDE's
- linear, quasilinear, nicht-linear
- elliptisch, parabolisch, hyperbolisch

2.) Quasilineare PDE
- Methode der Charakteristiken (Beispiele)

3.) Elliptische PDE
- Bsp: Laplace-Gleichung
- Harmonische Funktionen, Maximumsprinzip, Mittelwerts-Formel.
- Methode der Variablenseparation.

4.) Parabolische PDE
- Bsp: Wärmeleitungsgleichung
- Bsp: Inverse Wärmeleitungsgleichung
- Methode der Variablenseparation

5.) Hyperbolische PDE
- Bsp: Wellengleichung
- Formel von d'Alembert in (1+1)-Dimensionen
- Methode der Variablenseparation

6.) Green'sche Funktionen
- Rechnen mit der Dirac-Deltafunktion
- Idee der Green'schen Funktionen (Beispiele)

7.) Ausblick auf numerische Methoden
- 5-Punkt-Diskretisierung des Laplace-Operators (Beispiele)
LiteratureY. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005)

Zusätzliche Literatur:
Erwin Kreyszig, "Advanced Engineering Mathematics", John Wiley & Sons, Kap. 8, 11, 16 (sehr gutes Buch, als Referenz zu benutzen)
Norbert Hungerbühler, "Einführung in die partiellen Differentialgleichungen", vdf Hochschulverlag AG an der ETH Zürich.
G. Felder:Partielle Differenzialgleichungen.
Link
Prerequisites / NoticePrerequisites: Analysis I and II, Fourier series (Komplexe Analysis)
Electives
For the Bachelor in Interdisciplinary Sciences students can in principle choose from all subjects taught at the Bachelor level at ETH Zurich.



At the beginning of the 2. year an individual study programme is established for every student in discussion with the Director of Studies in interdisciplinary sciences. For details see Programme Regulations 2010.
NumberTitleTypeECTSHoursLecturers
401-2303-00LComplex Analysis Information W6 credits3V + 2UR. Pandharipande
AbstractComplex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, special functions, conformal mappings, Riemann mapping theorem.
ObjectiveWorking Knowledge with functions of one complex variables; in particular applications of the residue theorem
LiteratureTh. Gamelin: Complex Analysis. Springer 2001

E. Titchmarsh: The Theory of Functions. Oxford University Press

D. Salamon: "Funktionentheorie". Birkhauser, 2011. (In German)

L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co.

B. Palka: "An introduction to complex function theory."
Undergraduate Texts in Mathematics. Springer-Verlag, 1991.

R.Remmert: Theory of Complex Functions. Springer Verlag
Food Science Bachelor Information
1. Semester
First Year Examinations
NumberTitleTypeECTSHoursLecturers
401-0251-00LMathematics IO6 credits4V + 2UL. Halbeisen
AbstractThis course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.
ObjectiveMathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment.

The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses.
Content1. Single-Variable Calculus:
review of differentiation, linearisation, Taylor polynomials, maxima and minima, antiderivative, fundamental theorem of calculus, integration methods, improper integrals.

2. Linear Algebra and Complex Numbers:
systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra.

3. Ordinary Differential Equations:
separable ordinary differential equations (ODEs), integration by substitution, 1st and 2nd order linear ODEs, homogeneous systems of linear ODEs with constant coefficients, introduction to 2-dimensional dynamical systems.
Literature- Thomas, G. B.: Thomas' Calculus, Part 1 (Pearson Addison-Wesley).
- Bretscher, O.: Linear Algebra with Applications (Pearson Prentice Hall).
Prerequisites / NoticePrerequisites: familiarity with the basic notions from Calculus, in particular those of function and derivative.

Mathe-Lab (Assistance):
Mondays 12-14, Tuesdays 17-19, Wednesdays 17-19, in Room HG E 41.
3. Semester
Basic Courses II
Examination Block 1
NumberTitleTypeECTSHoursLecturers
701-0071-00LMathematics III: Systems AnalysisO4 credits2V + 1UN. Gruber, M. Vogt
AbstractThe objective of the systems analysis course is to deepen and illustrate the mathematical concepts on the basis of a series of very concrete examples. Topics covered include: linear box models with one or several variables, non-linear box models with one or several variables, time-discrete models, and continuous models in time and space.
ObjectiveLearning and applying of concepts (models) and quantitative methods to address concrete problems of environmental relevance. Understanding and applying the systems-analytic approach, i.e., Recognizing the core of the problem - simplification - quantitative approach - prediction.
ContentLink
Lecture notesOverhead slides will be made available through Ilias.
LiteratureImboden, D.S. and S. Pfenninger (2013) Introduction to Systems Analysis: Mathematically Modeling Natural Systems. Berlin Heidelberg: Springer Verlag.

Link
5. Semester
Food Science General Courses
NumberTitleTypeECTSHoursLecturers
752-1103-00LFood Analysis IIW+3 credits2VT. Gude
AbstractTo get acquainted with the principles and applications of mass spectrometry in food analytics.
ObjectiveTo get acquainted with the principles and applications of mass spectrometry in food analytics.
ContentMain focus: Mass spectrometry, applications of mass spectrometry (MS).
Lecture notesThe lectures are supplemented with handouts.
Electives (ONLY for Programme Regulations 2016)
A list with possible electives will be published separately.
NumberTitleTypeECTSHoursLecturers
551-1003-00LMethods of Biological Analysis Information W3 credits3GR. Aebersold, M. Badertscher, K. Weis
Abstract529-1042-00
Principles of the most important separation techniques and the interpretation of molecular spectra.

551-1003-00
The course will teach the basis and typical applications of methods for the analysis of nucleic acid sequences, mass spectrometric analysis of proteins and proteomes and advanced light and fluorescent imaging methods.
Objective529-1042-00
Knowledge of the necessary basics and the possibilities of application of the relevant spectroscopical and separation methods in analytical chermistry.

551-1003-00
Knowledge of the theoretical basis of the methods for nucleic acid sequence analysis, mass spectrometry based protein and proteome analysis and advanced light and fluorescent imaging methods, and an understanding of the application of these principles in experimental biology.
Content529-1042-00
Application oriented basics of instrumental analysis in organic chemistry and the empirical employment of the methods of structure elucidation (mass spectrometry, NMR-, IR-, UV/VIS spectroscopy). Basics and application of chromatographic and electrophoretic separation methods. Application of the knowledge by practising.

551-1003-00
The course will consist of lectures covering the theoretical and technical base of the respective analytical methods and of exercises where typical applications of the methods in modern experimental biology are discussed.
Lecture notes529-1042-00
A comprehensive script is available in the HCI-Shop. A summary of the part "Spektroskopie" defines the relevant material for the exam.

551-1003-00
Materials supporting the lectures and exercises will be made available via Moodle.
Literature529-1042-00
- Pretsch E., Bühlmann P., Badertscher M. Structure Determination of Organic Compounds, 5th revised and enlarged English edition, Springer-Verlag, Berlin 2009;
- Pretsch E., Bühlmann P., Badertscher M., Spektroskopische Daten zur Strukturaufklärung organischer Verbindungen, fünfte Auflage, Springer-Verlag, Berlin 2010;
- D.A. Skoog, J.J. Leary, Instrumentelle Analytik, Grundlagen, Geräte, Anwendungen, Springer, Berlin, 1996;
- K. Cammann, Instrumentelle Analytische Chemie, Verfahren, Anwendungen, Qualitätssicherung, Spektrum Akademischer Verlag, Heidelberg, 2001;
- R. Kellner, J.-M. Mermet, M. Otto, H.M. Widmer, Analytical Chemistry, Wiley-VCH Verlag, Weinheim, 1998;
- K. Robards, P.R.Haddad, P.E. Jackson, Principles and practice of modern chromatographic methods, Academic Press, London, 1994;
Prerequisites / Notice529-1042-00
Prerequisites:
- 529-1001-01 V "Allgemeine Chemie I (für Biol./Pharm.Wiss.)"
- 529-1001-00 P "Allgemeine Chemie I (für Biol./Pharm.Wiss.)"
- 529-1011-00 G "Organische Chemie I (für Biol./Pharm.Wiss.)"
Food Science Master Information
Major in Food Processing
Methodology Subjects
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W+5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
Major in Food Quality and Safety
Methodology Subjects
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W+5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
Major in Nutrition and Health
Methodology Subjects
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W+5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
Optional Subjects
NumberTitleTypeECTSHoursLecturers
766-6205-00LNutrient Analysis in Foods Restricted registration - show details
Number of participants limited to 15.
Permission from lecturers required for all students.
W3 credits3UM. B. Zimmermann, H. C. Winkler
AbstractIn this practical course different meals are prepared and then analysed in the laboratory. The analyses comprise energy, macronutrients, specific micronutrients as well as polyphenols and phytic acid. Based on these results, the nutritional value of each meal is critically evaluated and discussed.
ObjectiveLearning analytical methods to determine macro- and micronutrient content in foods. Critical evaluation of analytical results, critical comparison with values from food composition tables, and interpretation in relation to nutritional value of meals.
ContentThe practical course nutrient analysis in foods includes the meal preparation (2 hours in December 2017, date to be defined) and chemical analysis of five meals from 5 different types of diets (students will work in groups; one meal per group). The content of macronutrients, specific micronutrients and secondary plant components are analysed using common analytical methods. The analytical results are compared with calculated data from food composition databases by using the nutrition software EbisPro and critically evaluated. The nutritional values of the meals in relation to specific chronic diseases and iron bioavailability are discussed. The practical course is accompanied by a lecture on the basic principles of analytical chemistry.
Lecture notesA script and lecture slides are handed out before course start.
Prerequisites / NoticeStudents will work in groups.
Performance is assessed by a short test on course content, oral presentation of results and a short report.
Attendance is compulsory for the lecture, the laboratory work and the oral presentation.
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
752-1101-AALFood Analysis I
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-3 credits6RL. Nyström
AbstractTo understand the basic principles of analytical chemistry. To get acquainted with the principles and applications of important routine methods of instrumental food analysis (UV/VIS, IR, AAS, GC, HPLC).
ObjectiveTo understand the basic principles of analytical chemistry. To get acquainted with the principles and applications of important routine methods of instrumental food analysis (UV/VIS, IR, AAS, GC, HPLC).
ContentFundamentals: Chemical concentrations. The analytical process (sampling, sample preparation, calibration, measurement, statistical evaluation of analytical results). Errors in quantitative analysis. Important parameters of an analytical procedure (accuracy, precision, limit of detection, sensitivity, specificity/selectivity).

Methods: Optical spectroscopy (basic principles, UV/VIS, IR, and atomic absorption spectroscopy). Chromatography (GC, HPLC).
Lecture notesThe lectures are supplemented with handouts.
LiteratureFood Analysis - Fourth Edition, edited by S. Suzanne Nielson; 2010; Springer, Selected sections.
701-0071-AALMathematics III: Systems Analysis
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-4 credits9RN. Gruber
AbstractThe objective of the systems analysis course is to deepen and illustrate the mathematical concepts on the basis of a series of very concrete examples. Topics covered include: linear box models with one or several variables, non-linear box models with one or several variables, time-discrete models, and continuous models in time and space.
ObjectiveLearning and applying of concepts (models) and quantitative methods to address concrete problems of environmental relevance. Understanding and applying the systems-analytic approach, i.e., Recognizing the core of the problem - simplification - quantitative approach - prediction.
ContentLink
Lecture notesOverhead slides will be made available through Ilias.
LiteratureImboden, D.S. and S. Pfenninger (2013) Introduction to Systems Analysis: Mathematically Modeling Natural Systems. Berlin Heidelberg: Springer Verlag.

Link
MAS in Development and Cooperation Information
The lectures and advanced training courses of NADEL are accessible only for students of the MAS in Development and Cooperation and for qualified employees with at least two years experience in development cooperation and a Master's level or equivalent level of education as recognized by ETH. PhD students doing empirical research in development cooperation may be admitted "sur Dossier".
Advanced Training Courses
NumberTitleTypeECTSHoursLecturers
865-0000-06LImpact Analysis: Methods and Applications.
Only for MAS/CAS in Development and Cooperation students, as well as specialists with at least 24 months of practical experience in international cooperation.
Doctoral students dealing with empirical research in the area of development and cooperation (EZA) may be admitted "sur Dossier".

Registration only through the NADEL administration office.
W2 credits3GI. Günther
AbstractThe course gives an introduction to the most important methods for rigorous impact analysis of development programs and projects. The course is designed to both cover the most fundamental methods of impact analysis and introduce real world case studies from national, international and non-governmental development organizations and asks how rigorous impact analysis has influenced their policies.
ObjectiveParticipants understand the most important methods of impact analysis. They are able to conduct small scale studies to evaluate the impact of their own programs as well as manage larger impact evaluations for their organizations. Participants are able to use the results of own and external impact studies.
ContentIntroduction to rigorous impact analysis; Case studies and their policy implications; Introduction to the required statistical knowledge; Potentials and limitations of quantitative analysis; Experimental and quasi-experimental methods; Relevant and feasible indicators for the measurement of outcomes and impacts; Data collection and analysis; Project management of an impact analysis.
Prerequisites / NoticeStudents of the course must fulfil requirements specified on the homepage of NADEL. Electronic registration may be done only after registration with NADEL secretariate.
MAS in Nutrition and Health Information
Disciplinary Subjects
NumberTitleTypeECTSHoursLecturers
766-6205-00LNutrient Analysis in Foods Restricted registration - show details
Number of participants limited to 15.
Permission from lecturers required for all students.
W+3 credits3UM. B. Zimmermann, H. C. Winkler
AbstractIn this practical course different meals are prepared and then analysed in the laboratory. The analyses comprise energy, macronutrients, specific micronutrients as well as polyphenols and phytic acid. Based on these results, the nutritional value of each meal is critically evaluated and discussed.
ObjectiveLearning analytical methods to determine macro- and micronutrient content in foods. Critical evaluation of analytical results, critical comparison with values from food composition tables, and interpretation in relation to nutritional value of meals.
ContentThe practical course nutrient analysis in foods includes the meal preparation (2 hours in December 2017, date to be defined) and chemical analysis of five meals from 5 different types of diets (students will work in groups; one meal per group). The content of macronutrients, specific micronutrients and secondary plant components are analysed using common analytical methods. The analytical results are compared with calculated data from food composition databases by using the nutrition software EbisPro and critically evaluated. The nutritional values of the meals in relation to specific chronic diseases and iron bioavailability are discussed. The practical course is accompanied by a lecture on the basic principles of analytical chemistry.
Lecture notesA script and lecture slides are handed out before course start.
Prerequisites / NoticeStudents will work in groups.
Performance is assessed by a short test on course content, oral presentation of results and a short report.
Attendance is compulsory for the lecture, the laboratory work and the oral presentation.
MAS in Medical Physics Information
Specialization: General Medical Physics and Biomedical Engineering
Major in Bioimaging
Core Courses
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Electives
NumberTitleTypeECTSHoursLecturers
227-0391-00LMedical Image Analysis
Does not take place this semester.
W3 credits2GE. Konukoglu
AbstractIt is the objective of this lecture to introduce the basic concepts used
in Medical Image Analysis. In particular the lecture focuses on shape
representation schemes, segmentation techniques, and the various image registration methods commonly used in Medical Image Analysis applications.
ObjectiveThis lecture aims to give an overview of the basic concepts of Medical Image Analysis and its application areas.
Prerequisites / NoticeBasic knowledge of computer vision would be helpful.
227-0969-00LMethods & Models for fMRI Data Analysis Information W6 credits4VK. Stephan
AbstractThis course teaches methods and models for fMRI data analysis, covering all aspects of statistical parametric mapping (SPM), incl. preprocessing, the general linear model, statistical inference, multiple comparison corrections, event-related designs, and Dynamic Causal Modelling (DCM), a Bayesian framework for identification of nonlinear neuronal systems from neurophysiological data.
ObjectiveTo obtain in-depth knowledge of the theoretical foundations of SPM
and DCM and of their application to empirical fMRI data.
ContentThis course teaches state-of-the-art methods and models for fMRI data analysis. It covers all aspects of statistical parametric mapping (SPM), incl. preprocessing, the general linear model, frequentist and Bayesian inference, multiple comparison corrections, and event-related designs, and Dynamic Causal Modelling (DCM), a Bayesian framework for identification of nonlinear neuronal systems from neurophysiological data. A particular emphasis of the course will be on methodological questions arising in the context of studies in psychiatry, neurology and neuroeconomics.
MAS in Science, Technology and Policy Information
Core Courses
NumberTitleTypeECTSHoursLecturers
860-0002-00LQuantitative Policy Analysis and ModelingO6 credits4GA. Patt, T. Schmidt, E. Trutnevyte, O. van Vliet
AbstractThe lectures will introduce students to the principles of quantitative policy analysis, namely the methods to predict and evaluate the social, economic, and environmental effects of alternative strategies to achieve public objectives. A series of graded assignments will give students an opportunity for students to apply those methods to a set of case studies
ObjectiveThe objectives of this course are to develop the following key skills necessary for policy analysts:
- Identifying the critical quantitative factors that are of importance to policy makers in a range of decision-making situations.
- Developing conceptual models of the types of processes and relationships governing these quantitative factors, including stock-flow dynamics, feedback loops, optimization, sources and effects of uncertainty, and agent coordination problems.
- Develop and program numerical models to simulate the processes and relationships, in order to identify policy problems and the effects of policy interventions.
- Communicate the findings from these simulations and associated analysis in a manner that makes transparent their theoretical foundation, the level and sources of uncertainty, and ultimately their applicability to the policy problem.
The course will proceed through a series of policy analysis and modeling exercises, involving real-world or hypothetical problems. The specific examples around which work will be done will concern the environment, energy, health, and natural hazards management.
MAS in Sustainable Water Resources Information
The Master of Advanced Studies in Sustainable Water Resources is a 12 month full time postgraduate diploma programme. The focus of the programme is on issues of sustainability and water resources in Latin America, with special attention given to the impacts of development and climate change on water resources. The programme combines multidisciplinary coursework with high level research. Sample research topics include: water quality, water quantity, water for agriculture, water for the environment, adaptation to climate change, and integrated water resource management. Language: English. Credit hours: 66 ECTS.
For further information please visit: Link
Core Courses
Foundation courses: 12 credits have to be achieved.
NumberTitleTypeECTSHoursLecturers
102-0227-00LSystems Analysis and Mathematical Modeling in Urban Water Management Information W6 credits4GE. Morgenroth, M. Maurer
AbstractSystematic introduction of material balances, transport processes, kinetics, stoichiometry and conservation. Ideal reactors, residence time distribution, heterogeneous systems, dynamic response of reactors. Parameter identification, local sensitivity, error propagation, Monte Carlo simulation. Introduction to real time control (PID controllers). Extensive coding of examples in Berkeley Madonna.
ObjectiveThe goal of this course is to provide the students with an understanding and the tools to develop their own mathematical models, to plan experiments, to evaluate error propagation and to test simple process control strategies in the field of process engineering in urban water management.
ContentThe course will provide a broad introduction into the fundamentals of modeling water treatment systems. The topics are:
- Introduction into modeling and simulation
- The material balance equations, transport processes, transformation processes (kinetics, stoichiometry, conservation)
- Ideal reactors
- Hydraulic residence time distribution and modeling of real reactors
- Dynamic behavior of reactor systems
- Systems analytical tools: Sensitivity, parameter identification, error propagation, Monte Carlo simulation
- Introduction to process control (PID controller, fuzzy control)
Lecture notesCopies of overheads will be made available.
LiteratureThere will be a required textbook that students need to purchase:
Willi Gujer (2008): Systems Analysis for Water Technology. Springer-Verlag, Berlin Heidelberg
Prerequisites / NoticeThis course will be offered together with the course Process Engineering Ia. It is advantageous to follow both courses simultaneously.
Electives
Electives: 6 credits has to be achieved.
NumberTitleTypeECTSHoursLecturers
401-6215-00LUsing R for Data Analysis and Graphics (Part I) Information W1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the first part an introduction to the statistical software R for scientists. Topics covered are data generation and selection, graphical and basic statistical functions, creating simple functions, basic types of objects.
ObjectiveThe students will be able to use the software R for simple data analysis.
ContentThe course provides the first part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part I of the course covers the following topics:
- What is R?
- R Basics: reading and writing data from/to files, creating vectors & matrices, selecting elements of dataframes, vectors and matrices, arithmetics;
- Types of data: numeric, character, logical and categorical data, missing values;
- Simple (statistical) functions: summary, mean, var, etc., simple statistical tests;
- Writing simple functions;
- Introduction to graphics: scatter-, boxplots and other high-level plotting functions, embellishing plots by title, axis labels, etc., adding elements (lines, points) to existing plots.

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link

Note: Part I of UsingR is complemented and extended by Part II, which is offered during the second part of the semester and which can be taken independently from Part I.
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeThe course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
Mechanical Engineering Bachelor Information
1. Semester
Registration for the exercises via the application Link with your nETHz login (username, password).
First Year Examinations: Compulsory Courses
NumberTitleTypeECTSHoursLecturers
401-0261-G0LAnalysis I Information O8 credits5V + 3UA. Steiger
AbstractDifferential and integral calculus for functions of one and several variables; vector analysis; ordinary differential equations of first and of higher order, systems of ordinary differential equations; power series. The mathematical methods are applied in a large number of examples from mechanics, physics and other areas which are basic to engineering.
ObjectiveIntroduction to the mathematical foundations of engineering sciences, as far as concerning differential and integral calculus.
LiteratureU. Stammbach: Analysis I/II
Prerequisites / NoticeDie Übungsaufgaben (inkl. Multiple Choice) sind ein wichtiger Bestandteil der Lehrveranstaltung. Es wird erwartet, dass Sie mindestens 75% der wöchentlichen Serien bearbeiten und zur Korrektur einreichen.
3. Semester
Compulsory Courses
Examination Block 1
NumberTitleTypeECTSHoursLecturers
401-0363-10LAnalysis IIIO3 credits2V + 1UF. Da Lio
AbstractIntroduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics.
ObjectiveMathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations.

The first lecture is on Thursday, September 28 13-15 in HG F 7 and video transmitted into HG F 5.

The coordinator is Simon Brun
Link
ContentLaplace Transforms:
- Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting
- Transforms of Derivatives and Integrals, ODEs
- Unit Step Function, t-Shifting
- Short Impulses, Dirac's Delta Function, Partial Fractions
- Convolution, Integral Equations
- Differentiation and Integration of Transforms

Fourier Series, Integrals and Transforms:
- Fourier Series
- Functions of Any Period p=2L
- Even and Odd Functions, Half-Range Expansions
- Forced Oscillations
- Approximation by Trigonometric Polynomials
- Fourier Integral
- Fourier Cosine and Sine Transform

Partial Differential Equations:
- Basic Concepts
- Modeling: Vibrating String, Wave Equation
- Solution by separation of variables; use of Fourier series
- D'Alembert Solution of Wave Equation, Characteristics
- Heat Equation: Solution by Fourier Series
- Heat Equation: Solutions by Fourier Integrals and Transforms
- Modeling Membrane: Two Dimensional Wave Equation
- Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series
- Solution of PDEs by Laplace Transform
Lecture notesLecture notes by Prof. Dr. Alessandra Iozzi:
Link
LiteratureE. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011

C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed.

S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY.

G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003.

Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005

For reference/complement of the Analysis I/II courses:

Christian Blatter: Ingenieur-Analysis
Link
5. Semester
Focus Specialization
Design, Mechanics and Materials
Focus Coordinator: Prof. Kristina Shea
In order to achieve the required 20 credit points for the Focus Specialization Design, Mechanics and Material you are free to choose any of the courses offered within the focus and are encouraged to select among those recommended. If you wish to take one of the Master level courses, you must get approval from the lecturer.
NumberTitleTypeECTSHoursLecturers
151-0360-00LProcedures for the Analysis of StructuresW+4 credits2V + 1UG. Kress
AbstractBasic theories for structure integrity calculations are presented with focus on strength, stability, fatigue and elasto-plastic structural analysis.
Theories and models for one dimesional and planar structures are presented based on energy theorems.
ObjectiveBasic principles applied in structural mechanics. Introduction to the theories of planar structures. Development of an understanding of the relationship between material properties, structural theories and design criteria.
Content1. Basic problem of continuum mechanics and energy principles: structural theories, homogenization theories; finite elements; fracture mechanics.
2.Structural theories for planar structures and stability: plane-stress, plate theory, buckling of plates (non-linear plate theory).
3.Strength of material theories and material properties: ductile behaviour, plasticity, von Mises, Tresca, principal stress criterion; brittle behaviour; viscoplastic behaviour, creep resistance.
4. Structural design: fatigue and dynamic structural analysis.
Lecture notesScript and all other course material available on MOODLE
Prerequisites / Noticenone
Engineering Tools IV
The participation at the Engineering Tools course is mandatory. If you miss any classes, no credit points will be awarded. For exemptions you have to contact the lecturer of the course.
NumberTitleTypeECTSHoursLecturers
151-0015-10LEngineering Tool IV: Experimental Modal Analysis Restricted registration - show details
All Engineering Tool courses are for MAVT-Bachelor students only.

Number of participants limited to 16.

Only one course can be chosen per semester.
W0.4 credits1KF. Kuster
AbstractMeasuring- and analysis-methods for the determination of transfer functions of mechanical structures. Evaluation and preparation of the measured data for visualisation and interpretation of the dynamic behaviour.
ObjectiveIntroduction into the practical application of measuring- and analysis-methods for determination of transfer functions of mechanical structures. Evaluation and preparation of the measured data for visualisation and interpretation of the dynamic behaviour.
ContentAcquaintance with the acceleration- and force-sensors, measurement of transfer functions of mechanical structures, determination and description of modes of vibration by means of practical examples, introduction into the vibration theory and its fundamental terms, discrete oscillator.
Lecture notesyes, distribution in the course (CHF 20.-)
LiteratureDavid Ewins, Modal Testing: Theory and Practice
Prerequisites / NoticeIn the practical part of the course the participants self will make measurements on structures and then analyse them for eigenfrequencies and modes of vibrations.
Mechanical Engineering Master Information
Core Courses
Energy, Flows and Processes
The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.
NumberTitleTypeECTSHoursLecturers
101-0187-00LStructural Reliability and Risk Analysis Information W3 credits2GS. Marelli
AbstractStructural reliability aims at quantifying the probability of failure of systems due to uncertainties in their design, manufacturing and environmental conditions. Risk analysis combines this information with the consequences of failure in view of optimal decision making. The course presents the underlying probabilistic modelling and computational methods for reliability and risk assessment.
ObjectiveThe goal of this course is to provide the students with a thorough understanding of the key concepts behind structural reliability and risk analysis. After this course the students will have refreshed their knowledge of probability theory and statistics to model uncertainties in view of engineering applications. They will be able to analyze the reliability of a structure and to use risk assessment methods for decision making under uncertain conditions. They will be aware of the state-of-the-art computational methods and software in this field.
ContentEngineers are confronted every day to decision making under limited amount of information and uncertain conditions. When designing new structures and systems, the design codes such as SIA or Euro- codes usually provide a framework that guarantees safety and reliability. However the level of safety is not quantified explicitly, which does not allow the analyst to properly choose between design variants and evaluate a total cost in case of failure. In contrast, the framework of risk analysis allows one to incorporate the uncertainty in decision making.

The first part of the course is a reminder on probability theory that is used as a main tool for reliability and risk analysis. Classical concepts such as random variables and vectors, dependence and correlation are recalled. Basic statistical inference methods used for building a probabilistic model from the available data, e.g. the maximum likelihood method, are presented.

The second part is related to structural reliability analysis, i.e. methods that allow one to compute probabilities of failure of a given system with respect to prescribed criteria. The framework of reliability analysis is first set up. Reliability indices are introduced together with the first order-second moment method (FOSM) and the first order reliability method (FORM). Methods based on Monte Carlo simulation are then reviewed and illustrated through various examples. By-products of reliability analysis such as sensitivity measures and partial safety coefficients are derived and their links to structural design codes is shown. The reliability of structural systems is also introduced as well as the methods used to reassess existing structures based on new information.

The third part of the course addresses risk assessment methods. Techniques for the identification of hazard scenarios and their representation by fault trees and event trees are described. Risk is defined with respect to the concept of expected utility in the framework of decision making. Elements of Bayesian decision making, i.e. pre-, post and pre-post risk assessment methods are presented.

The course also includes a tutorial using the UQLab software dedicated to real world structural reliability analysis.
Lecture notesSlides of the lectures are available online every week. A printed version of the full set of slides is proposed to the students at the beginning of the semester.
LiteratureAng, A. and Tang, W.H, Probability Concepts in Engineering - Emphasis on Applications to Civil and Environmental Engineering, 2nd Edition, John Wiley & Sons, 2007.

S. Marelli, R. Schöbi, B. Sudret, UQLab user manual - Structural reliability (rare events estimation), Report UQLab-V0.92-107.
Prerequisites / NoticeBasic course on probability theory and statistics
Mechanics, Materials, Structures
The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.
NumberTitleTypeECTSHoursLecturers
151-0360-00LProcedures for the Analysis of StructuresW4 credits2V + 1UG. Kress
AbstractBasic theories for structure integrity calculations are presented with focus on strength, stability, fatigue and elasto-plastic structural analysis.
Theories and models for one dimesional and planar structures are presented based on energy theorems.
ObjectiveBasic principles applied in structural mechanics. Introduction to the theories of planar structures. Development of an understanding of the relationship between material properties, structural theories and design criteria.
Content1. Basic problem of continuum mechanics and energy principles: structural theories, homogenization theories; finite elements; fracture mechanics.
2.Structural theories for planar structures and stability: plane-stress, plate theory, buckling of plates (non-linear plate theory).
3.Strength of material theories and material properties: ductile behaviour, plasticity, von Mises, Tresca, principal stress criterion; brittle behaviour; viscoplastic behaviour, creep resistance.
4. Structural design: fatigue and dynamic structural analysis.
Lecture notesScript and all other course material available on MOODLE
Prerequisites / Noticenone
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Robotics, Systems and Control
The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Micro & Nanosystems
The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.
NumberTitleTypeECTSHoursLecturers
227-0377-00LPhysics of Failure and Failure Analysis of Electronic Devices and EquipmentW3 credits2VU. Sennhauser
AbstractFailures have to be avoided by proper design, material selection and manufacturing. Properties, degradation mechanisms, and expected lifetime of materials are introduced and the basics of failure analysis and analysis equipment are presented. Failures will be demonstrated experimentally and the opportunity is offered to perform a failure analysis with advanced equipment in the laboratory.
ObjectiveIntroduction to the degradation and failure mechanisms and causes of electronic components, devices and systems as well as to methods and tools of reliability testing, characterization and failure analysis.
ContentSummary of reliability and failure analysis terminology; physics of failure: materials properties, physical processes and failure mechanisms; failure analysis of ICs, PCBs, opto-electronics, discrete and other components and devices; basics and properties of instruments; application in circuit design and reliability analysis
Lecture notesComprehensive copy of transparencies
Bioengineering
The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
406-0353-AALAnalysis III Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-4 credits9RF. Da Lio
AbstractIntroduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics.
ObjectiveMathematical treatment of problems in science and engineering. To understand the properties of the different types of partlial differentail equations.
ContentLaplace Transforms:
- Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting
- Transforms of Derivatives and Integrals, ODEs
- Unit Step Function, t-Shifting
- Short Impulses, Dirac's Delta Function, Partial Fractions
- Convolution, Integral Equations
- Differentiation and Integration of Transforms

Fourier Series, Integrals and Transforms:
- Fourier Series
- Functions of Any Period p=2L
- Even and Odd Functions, Half-Range Expansions
- Forced Oscillations
- Approximation by Trigonometric Polynomials
- Fourier Integral
- Fourier Cosine and Sine Transform

Partial Differential Equations:
- Basic Concepts
- Modeling: Vibrating String, Wave Equation
- Solution by separation of variables; use of Fourier series
- D'Alembert Solution of Wave Equation, Characteristics
- Heat Equation: Solution by Fourier Series
- Heat Equation: Solutions by Fourier Integrals and Transforms
- Modeling Membrane: Two Dimensional Wave Equation
- Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series
- Solution of PDEs by Laplace Transform
LiteratureE. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011

C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed.
Stanley J. Farlow, Partial Differential Equations for Scientists and Engineers, (Dover Books on Mathematics).

G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003.

Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005

For reference/complement of the Analysis I/II courses:

Christian Blatter: Ingenieur-Analysis (Download PDF)
Prerequisites / NoticeUp-to-date information about this course can be found at:
Link
Materials Science Bachelor Information
1. Semester
Basis Courses Part 1
First Year Examinations
NumberTitleTypeECTSHoursLecturers
401-0261-GULAnalysis I Information O8 credits5V + 3UA. Steiger
AbstractDifferential and integral calculus for functions of one and several variables; vector analysis; ordinary differential equations of first and of higher order, systems of ordinary differential equations; power series. The mathematical methods are applied in a large number of examples from mechanics, physics and other areas which are basic to engineering.
ObjectiveIntroduction to the mathematical foundations of engineering sciences, as far as concerning differential and integral calculus.
LiteratureU. Stammbach: Analysis I/II
Prerequisites / NoticeDie Übungsaufgaben (inkl. Multiple Choice) sind ein wichtiger Bestandteil der Lehrveranstaltung. Es wird erwartet, dass Sie mindestens 75% der wöchentlichen Serien bearbeiten und zur Korrektur einreichen.
3. Semester
Basic Courses Part 2
Examination Block 2
NumberTitleTypeECTSHoursLecturers
401-0363-10LAnalysis IIIO3 credits2V + 1UF. Da Lio
AbstractIntroduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics.
ObjectiveMathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations.

The first lecture is on Thursday, September 28 13-15 in HG F 7 and video transmitted into HG F 5.

The coordinator is Simon Brun
Link
ContentLaplace Transforms:
- Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting
- Transforms of Derivatives and Integrals, ODEs
- Unit Step Function, t-Shifting
- Short Impulses, Dirac's Delta Function, Partial Fractions
- Convolution, Integral Equations
- Differentiation and Integration of Transforms

Fourier Series, Integrals and Transforms:
- Fourier Series
- Functions of Any Period p=2L
- Even and Odd Functions, Half-Range Expansions
- Forced Oscillations
- Approximation by Trigonometric Polynomials
- Fourier Integral
- Fourier Cosine and Sine Transform

Partial Differential Equations:
- Basic Concepts
- Modeling: Vibrating String, Wave Equation
- Solution by separation of variables; use of Fourier series
- D'Alembert Solution of Wave Equation, Characteristics
- Heat Equation: Solution by Fourier Series
- Heat Equation: Solutions by Fourier Integrals and Transforms
- Modeling Membrane: Two Dimensional Wave Equation
- Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series
- Solution of PDEs by Laplace Transform
Lecture notesLecture notes by Prof. Dr. Alessandra Iozzi:
Link
LiteratureE. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011

C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed.

S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY.

G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003.

Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005

For reference/complement of the Analysis I/II courses:

Christian Blatter: Ingenieur-Analysis
Link
Mathematics Bachelor Information
First Year Compulsory Courses
First Year Examination Block 2
NumberTitleTypeECTSHoursLecturers
401-1261-07LAnalysis I Information O10 credits6V + 3UM. Einsiedler
AbstractIntroduction to the differential and integral calculus in one real variable: fundaments of mathematical thinking, numbers, sequences, basic point set topology, continuity, differentiable functions, ordinary differential equations, Riemann integration.
ObjectiveThe ability to work with the basics of calculus in a mathematically rigorous way.
LiteratureH. Amann, J. Escher: Analysis I
Link

J. Appell: Analysis in Beispielen und Gegenbeispielen
Link

R. Courant: Vorlesungen über Differential- und Integralrechnung
Link

O. Forster: Analysis 1
Link

H. Heuser: Lehrbuch der Analysis
Link

K. Königsberger: Analysis 1
Link

W. Walter: Analysis 1
Link

V. Zorich: Mathematical Analysis I (englisch)
Link

A. Beutelspacher: "Das ist o.B.d.A. trivial"
Link

H. Schichl, R. Steinbauer: Einführung in das mathematische Arbeiten
Link
Compulsory Courses
Examination Block I
In Examination Block I either the course unit 402-2883-00L Physics III or the course unit 402-2203-01L Classical Mechanics must be chosen and registered for an examination. (Students may also enrol for the other of the two course units; within the ETH Bachelor's programme in mathematics, this other course unit cannot be registered in myStudies for an examination nor can it be recognised for the Bachelor's degree.)
NumberTitleTypeECTSHoursLecturers
401-2303-00LComplex Analysis Information O6 credits3V + 2UR. Pandharipande
AbstractComplex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, special functions, conformal mappings, Riemann mapping theorem.
ObjectiveWorking Knowledge with functions of one complex variables; in particular applications of the residue theorem
LiteratureTh. Gamelin: Complex Analysis. Springer 2001

E. Titchmarsh: The Theory of Functions. Oxford University Press

D. Salamon: "Funktionentheorie". Birkhauser, 2011. (In German)

L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co.

B. Palka: "An introduction to complex function theory."
Undergraduate Texts in Mathematics. Springer-Verlag, 1991.

R.Remmert: Theory of Complex Functions. Springer Verlag
Core Courses
Core Courses: Pure Mathematics
NumberTitleTypeECTSHoursLecturers
401-3461-00LFunctional Analysis I Information
At most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics.
W10 credits4V + 1UA. Carlotto
AbstractBaire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications.
ObjectiveAcquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
Lecture notesLecture Notes on "Funktionalanalysis I" by Michael Struwe
LiteratureA primary reference for the course is the textbook by H. Brezis:

Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

Other useful, and recommended references are the following:

Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
Prerequisites / NoticeSolid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces).
Electives
Selection: Probability Theory, Statistics
NumberTitleTypeECTSHoursLecturers
401-4623-00LTime Series Analysis
Does not take place this semester.
W6 credits3Gnot available
AbstractStatistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R.
ObjectiveUnderstanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.
ContentThis course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations.
Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R.
Lecture notesNot available
LiteratureA list of references will be distributed during the course.
Prerequisites / NoticeBasic knowledge in probability and statistics
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
Seminars
Early enrolments for seminars in myStudies are encouraged, so that we will recognize need for additional seminars in a timely manner. Some seminars have waiting lists. Nevertheless, register for at most two mathematics seminars. In this case, you express a stronger preference for the seminar for which you register earlier.
NumberTitleTypeECTSHoursLecturers
401-3680-67LPersistent Homology and Topological Data Analysis Restricted registration - show details
Number of participants limited to 8.
W4 credits2SP. S. Jossen
AbstractWe study the fundamental tools of topological data analysis: Persistent homology, persistence modules and barcodes. Our goal is to read and understand parts of the paper "Principal Component Analysis of Persistent Homology..." by Vanessa Robins and Kate Turner (ArXiV 1507.01454v1).
ObjectiveTo get familiar with the basic concepts of topological data analysis and see some applications thereof.
LiteratureHerbert Edelsbrunner and John L. Harer: Computational Topology, An Introduction. AMS 2010
Prerequisites / NoticeParticipants are supposed to be familiar with singular homology.
401-3650-67LNumerical Analysis Seminar: Tensor Numerics and Deep Neural Networks Information Restricted registration - show details
Number of participants limited to 10.
W4 credits2SC. Schwab
AbstractThe seminar addresses recently discovered
_mathematical_ connections between Deep Learning
and Tensor-formatted numerical analysis,
with particular attention to
the numerical solution of partial differential equations,
with random input data.
ObjectiveThe aim of the seminar is to review recent [2015-]
research work and results,
together with recently published software
such as the TT-Toolbox, and Google's TENSORFLOW.

The focus is on the mathematical analysis and
interpretation of current learning approaches
and related mathematical and technical fields, e.g.
high-dimensional approximation, tensor structured numerical methods
for the numerical solution of highdimensional PDEs,
with applications in computational UQ.
For theory, we refer to the references in the survey
Link
Numerical experiments will be done with TENSORFLOW and with the
TT toolbox at
Link
Lecture notesThe seminar will study a set of 10 orginial papers from 2015 to today.
LiteratureHelmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen
Optimal Approximation with Sparsely Connected Deep Neural Networks
arXiv:1705.01714

N. Cohen, O. Sharir, Y. Levine, R. Tamari, D. Yakira and A. Shashua (May 2017):
Analysis and design of convolutional networks via hierarchical tensor decompositions,
arXiv:1705.02302v3.

N. Cohen and A. Shashua (March 2016),
Convolutional rectifier networks as generalized tensor decompositions,
Technical report, arXiv:1603.00162.
Proceedings of The 33rd International Conference on Machine Learning, pp. 955-963, 2016.

N. Cohen, O. Sharir and A. Shashua (Sept. 2015),
On the expressive power of deep learning: A tensor analysis,
Technical report, arXiv:1509.05009.
Journal-ref: 29th Annual Conference on Learning Theory, pp. 698-728, 2016.
Prerequisites / NoticeCompleted BSc MATH exam.
Mathematics Master Information
Core Courses
For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.
Bachelor Core Courses: Pure Mathematics
Further restrictions apply, but in particular:
401-3531-00L Differential Geometry I can only be recognised for the Master Programme if 401-3532-00L Differential Geometry II has not been recognised for the Bachelor Programme.
Analogously for:
401-3461-00L Functional Analysis I - 401-3462-00L Functional Analysis II
401-3001-61L Algebraic Topology I - 401-3002-12L Algebraic Topology II
401-3132-00L Commutative Algebra - 401-3146-12L Algebraic Geometry
401-3371-00L Dynamical Systems I - 401-3372-00L Dynamical Systems II
For the category assignment take contact with the Study Administration Office (Link) after having received the credits.
NumberTitleTypeECTSHoursLecturers
401-3461-00LFunctional Analysis I Information
At most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics.
E-10 credits4V + 1UA. Carlotto
AbstractBaire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications.
ObjectiveAcquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
Lecture notesLecture Notes on "Funktionalanalysis I" by Michael Struwe
LiteratureA primary reference for the course is the textbook by H. Brezis:

Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

Other useful, and recommended references are the following:

Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
Prerequisites / NoticeSolid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces).
Electives
For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.
Electives: Applied Mathematics and Further Application-Oriented Fields
¬
Selection: Numerical Analysis
NumberTitleTypeECTSHoursLecturers
401-4657-00LNumerical Analysis of Stochastic Ordinary Differential Equations Information
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
W6 credits3V + 1UA. Jentzen
AbstractCourse on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.
ObjectiveThe aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.
ContentGeneration of random numbers
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Multilevel Monte Carlo methods for SODEs
Applications to computational finance: Option valuation
Lecture notesLecture Notes are available in the lecture homepage (please follow the link in the Learning materials section).
LiteratureP. Glassermann:
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.

P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
Prerequisites / NoticePrerequisites:

Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.

a) mandatory courses:
Elementary Probability,
Probability Theory I.

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday, September 20, 2017

Date of the End-of-Semester examination: Wednesday, December 20, 2017, 13:00-15:00; students must arrive before 12:30 at ETH HG E 19.
Room for the End-of-Semester examination: ETH HG E 19.

Exam inspection: Monday, March 5, 2018,
13:00-14:00 at HG D 5.1
Please bring your legi.
Selection: Probability Theory, Statistics
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
401-4623-00LTime Series Analysis
Does not take place this semester.
W6 credits3Gnot available
AbstractStatistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R.
ObjectiveUnderstanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.
ContentThis course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations.
Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R.
Lecture notesNot available
LiteratureA list of references will be distributed during the course.
Prerequisites / NoticeBasic knowledge in probability and statistics
Application Area
Only necessary and eligible for the Master degree in Applied Mathematics.
One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area.
Image Processing and Computer Vision
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
Seminars and Semester Papers
Seminars
Early enrolments for seminars in myStudies are encouraged, so that we will recognize need for additional seminars in a timely manner. Some seminars have waiting lists. Nevertheless, register for at most two mathematics seminars. In this case, you express a stronger preference for the seminar for which you register earlier.
NumberTitleTypeECTSHoursLecturers
401-3680-67LPersistent Homology and Topological Data Analysis Restricted registration - show details
Number of participants limited to 8.
W4 credits2SP. S. Jossen
AbstractWe study the fundamental tools of topological data analysis: Persistent homology, persistence modules and barcodes. Our goal is to read and understand parts of the paper "Principal Component Analysis of Persistent Homology..." by Vanessa Robins and Kate Turner (ArXiV 1507.01454v1).
ObjectiveTo get familiar with the basic concepts of topological data analysis and see some applications thereof.
LiteratureHerbert Edelsbrunner and John L. Harer: Computational Topology, An Introduction. AMS 2010
Prerequisites / NoticeParticipants are supposed to be familiar with singular homology.
401-3650-67LNumerical Analysis Seminar: Tensor Numerics and Deep Neural Networks Information Restricted registration - show details
Number of participants limited to 10.
W4 credits2SC. Schwab
AbstractThe seminar addresses recently discovered
_mathematical_ connections between Deep Learning
and Tensor-formatted numerical analysis,
with particular attention to
the numerical solution of partial differential equations,
with random input data.
ObjectiveThe aim of the seminar is to review recent [2015-]
research work and results,
together with recently published software
such as the TT-Toolbox, and Google's TENSORFLOW.

The focus is on the mathematical analysis and
interpretation of current learning approaches
and related mathematical and technical fields, e.g.
high-dimensional approximation, tensor structured numerical methods
for the numerical solution of highdimensional PDEs,
with applications in computational UQ.
For theory, we refer to the references in the survey
Link
Numerical experiments will be done with TENSORFLOW and with the
TT toolbox at
Link
Lecture notesThe seminar will study a set of 10 orginial papers from 2015 to today.
LiteratureHelmut Bölcskei, Philipp Grohs, Gitta Kutyniok, Philipp Petersen
Optimal Approximation with Sparsely Connected Deep Neural Networks
arXiv:1705.01714

N. Cohen, O. Sharir, Y. Levine, R. Tamari, D. Yakira and A. Shashua (May 2017):
Analysis and design of convolutional networks via hierarchical tensor decompositions,
arXiv:1705.02302v3.

N. Cohen and A. Shashua (March 2016),
Convolutional rectifier networks as generalized tensor decompositions,
Technical report, arXiv:1603.00162.
Proceedings of The 33rd International Conference on Machine Learning, pp. 955-963, 2016.

N. Cohen, O. Sharir and A. Shashua (Sept. 2015),
On the expressive power of deep learning: A tensor analysis,
Technical report, arXiv:1509.05009.
Journal-ref: 29th Annual Conference on Learning Theory, pp. 698-728, 2016.
Prerequisites / NoticeCompleted BSc MATH exam.
Additional Courses
NumberTitleTypeECTSHoursLecturers
401-5350-00LAnalysis Seminar Information E-0 credits1KM. Struwe, A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, T. Ilmanen, T. Kappeler, T. Rivière, D. A. Salamon
AbstractResearch colloquium
Objective
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
406-2303-AALComplex Analysis Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-6 credits13RR. Pandharipande
AbstractComplex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, conformal mappings, Riemann mapping theorem.
Objective
LiteratureL. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co.

B. Palka: "An introduction to complex function theory."
Undergraduate Texts in Mathematics. Springer-Verlag, 1991.

R.Remmert: Theory of Complex Functions.. Springer Verlag

E.Hille: Analytic Function Theory. AMS Chelsea Publication
406-3461-AALFunctional Analysis I
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-10 credits21RA. Carlotto
AbstractBaire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications.
ObjectiveAcquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
Lecture notesLecture Notes on "Funktionalanalysis I" by Michael Struwe.
LiteratureA primary reference for the course is the textbook by H. Brezis:

Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

Other useful, and recommended references are the following:

Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
Micro- and Nanosystems Master Information
Core Courses
Elective Core Courses
NumberTitleTypeECTSHoursLecturers
227-0377-00LPhysics of Failure and Failure Analysis of Electronic Devices and EquipmentW3 credits2VU. Sennhauser
AbstractFailures have to be avoided by proper design, material selection and manufacturing. Properties, degradation mechanisms, and expected lifetime of materials are introduced and the basics of failure analysis and analysis equipment are presented. Failures will be demonstrated experimentally and the opportunity is offered to perform a failure analysis with advanced equipment in the laboratory.
ObjectiveIntroduction to the degradation and failure mechanisms and causes of electronic components, devices and systems as well as to methods and tools of reliability testing, characterization and failure analysis.
ContentSummary of reliability and failure analysis terminology; physics of failure: materials properties, physical processes and failure mechanisms; failure analysis of ICs, PCBs, opto-electronics, discrete and other components and devices; basics and properties of instruments; application in circuit design and reliability analysis
Lecture notesComprehensive copy of transparencies
Neural Systems and Computation Master Information
Core Courses
Compulsory Core Courses
NumberTitleTypeECTSHoursLecturers
227-1039-00LBasics of Instrumentation, Measurement, and Analysis (University of Zurich) Restricted registration - show details
No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH.
UZH Module Code: INI502

Mind the enrolment deadlines at UZH:
Link

Registration in this class requires the permission of the instructors. Class size will be limited to available lab spots.
Preference is given to students that require this class as part of their major.
O4 credits9SS.‑C. Liu, T. Delbrück, R. Hahnloser, G. Indiveri, V. Mante, P. Pyk, W. von der Behrens
AbstractExperimental data are always as good as the instrumentation and measurement, but never any better. This course provides the very basics of instrumentation relevant to neurophysiology and neuromorphic engineering, it consists of two parts: a common introductory part involving analog signals and their acquisition (Part I), and a more specialized second part (Part II).
ObjectiveThe goal of Part I is to provide a general introduction to the signal acquisition process. Students are familiarized with basic lab equipment such as oscilloscopes, function generators, and data acquisition devices. Different electrical signals are generated, visualized, filtered, digitized, and analyzed using Matlab (Mathworks Inc.) or Labview (National Instruments).

In Part II, the students are divided into small groups to work on individual measurement projects according to availability and interest. Students single-handedly solve a measurement task, making use of their basic knowledge acquired in the first part. Various signal sources will be provided.
Prerequisites / NoticeFor each part, students must hand in a written report and present a live demonstration of their measurement setup to the respective supervisor. The supervisor of Part I is the teaching assistant, and the supervisor of Part II is task specific. Admission to Part II is conditional on completion of Part I (report + live demonstration).

Reports must contain detailed descriptions of the measurement goal, the measurement procedure, and the measurement outcome. Either confidence or significance of measurements must be provided. Acquisition and analysis software must be documented.
Physics Bachelor Information
First Year Compulsory Courses
First Year Examination Block 2
NumberTitleTypeECTSHoursLecturers
401-1261-07LAnalysis I Information O10 credits6V + 3UM. Einsiedler
AbstractIntroduction to the differential and integral calculus in one real variable: fundaments of mathematical thinking, numbers, sequences, basic point set topology, continuity, differentiable functions, ordinary differential equations, Riemann integration.
ObjectiveThe ability to work with the basics of calculus in a mathematically rigorous way.
LiteratureH. Amann, J. Escher: Analysis I
Link

J. Appell: Analysis in Beispielen und Gegenbeispielen
Link

R. Courant: Vorlesungen über Differential- und Integralrechnung
Link

O. Forster: Analysis 1
Link

H. Heuser: Lehrbuch der Analysis
Link

K. Königsberger: Analysis 1
Link

W. Walter: Analysis 1
Link

V. Zorich: Mathematical Analysis I (englisch)
Link

A. Beutelspacher: "Das ist o.B.d.A. trivial"
Link

H. Schichl, R. Steinbauer: Einführung in das mathematische Arbeiten
Link
Compulsory Courses
Second Year Compulsory Courses
Examination Block I
NumberTitleTypeECTSHoursLecturers
401-2303-00LComplex Analysis Information O6 credits3V + 2UR. Pandharipande
AbstractComplex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, special functions, conformal mappings, Riemann mapping theorem.
ObjectiveWorking Knowledge with functions of one complex variables; in particular applications of the residue theorem
LiteratureTh. Gamelin: Complex Analysis. Springer 2001

E. Titchmarsh: The Theory of Functions. Oxford University Press

D. Salamon: "Funktionentheorie". Birkhauser, 2011. (In German)

L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co.

B. Palka: "An introduction to complex function theory."
Undergraduate Texts in Mathematics. Springer-Verlag, 1991.

R.Remmert: Theory of Complex Functions. Springer Verlag
Selection of Higher Semester Courses
NumberTitleTypeECTSHoursLecturers
401-3461-00LFunctional Analysis I Information
At most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics.
W10 credits4V + 1UA. Carlotto
AbstractBaire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications.
ObjectiveAcquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
Lecture notesLecture Notes on "Funktionalanalysis I" by Michael Struwe
LiteratureA primary reference for the course is the textbook by H. Brezis:

Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

Other useful, and recommended references are the following:

Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
Prerequisites / NoticeSolid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces).
Physics Master Information
Electives
Electives: Physics and Mathematics
Selection: Mathematics
NumberTitleTypeECTSHoursLecturers
401-3461-00LFunctional Analysis I Information
At most one of the three course units (Bachelor Core Courses)
401-3461-00L Functional Analysis I
401-3531-00L Differential Geometry I
401-3601-00L Probability Theory
can be recognised for the Master's degree in Mathematics or Applied Mathematics.
W10 credits4V + 1UA. Carlotto
AbstractBaire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications.
ObjectiveAcquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
Lecture notesLecture Notes on "Funktionalanalysis I" by Michael Struwe
LiteratureA primary reference for the course is the textbook by H. Brezis:

Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

Other useful, and recommended references are the following:

Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
Prerequisites / NoticeSolid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces).
Quantitative Finance Master Information
see Link

Students in the Joint Degree Master's Programme "Quantitative Finance" must book University of Zurich modules directly at the University of Zurich. Those modules are not listed here.
Elective Courses
Mathematical Methods for Finance
For possible additional course offerings see Link
NumberTitleTypeECTSHoursLecturers
401-4657-00LNumerical Analysis of Stochastic Ordinary Differential Equations Information
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
W6 credits3V + 1UA. Jentzen
AbstractCourse on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.
ObjectiveThe aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.
ContentGeneration of random numbers
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Multilevel Monte Carlo methods for SODEs
Applications to computational finance: Option valuation
Lecture notesLecture Notes are available in the lecture homepage (please follow the link in the Learning materials section).
LiteratureP. Glassermann:
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.

P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
Prerequisites / NoticePrerequisites:

Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.

a) mandatory courses:
Elementary Probability,
Probability Theory I.

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday, September 20, 2017

Date of the End-of-Semester examination: Wednesday, December 20, 2017, 13:00-15:00; students must arrive before 12:30 at ETH HG E 19.
Room for the End-of-Semester examination: ETH HG E 19.

Exam inspection: Monday, March 5, 2018,
13:00-14:00 at HG D 5.1
Please bring your legi.
Spatial Development and Infrastructure Systems Master Information
1. Semester
Major Courses
Major in Spatial and Landscape Development
NumberTitleTypeECTSHoursLecturers
103-0307-00LMulti-Criteria Decision Analysis Information W3 credits2GA. Grêt-Regamey
AbstractPlanners need to make decisions about the best possible mix of land uses. With increasing availability of spatial databases and the analytical capabilities of GIS, more effective decision support systems can be developed. The goal of the course is to provide the basics of spatial analysis and to teach the integration of spatial data into multicriteria decision-making systems.
ObjectiveThis course will:
1) introduce students to techniques and issues associated with spatial modeling and decision support systems, including analytical techniques that are unique to spatial analysis
2) provide hands-on training in the use of these spatial tools in R while addressing real planning problems.

The emphasis is on concepts, resources, and analysis tools that students can use in science, private companies and government careers.
Lecture notes- Handouts of the lectures
- Script
- Exercise material

Download: Link
Prerequisites / NoticeThe course will presume basic knowledge of the R software package. RE&IS Master students will acquire this knowledge during the
"Basics of RE&IS" (103-0377-10L) course. Provided there are still available places, students from other disciplines can also join the part of "Basics of RE&IS" in which R is taught (i.e. first five lectures; no credit points will be awarded). These students can register for "Basics of RE&IS" by e-mailing Maarten van Strien (Link). Alternatively, they can acquire basic R knowledge with online tutorials, such as "Introduction to R" by W. N. Venables and D. M. Smith available online at Link.
Network Infrastructure
NumberTitleTypeECTSHoursLecturers
101-0187-00LStructural Reliability and Risk Analysis Information W3 credits2GS. Marelli
AbstractStructural reliability aims at quantifying the probability of failure of systems due to uncertainties in their design, manufacturing and environmental conditions. Risk analysis combines this information with the consequences of failure in view of optimal decision making. The course presents the underlying probabilistic modelling and computational methods for reliability and risk assessment.
ObjectiveThe goal of this course is to provide the students with a thorough understanding of the key concepts behind structural reliability and risk analysis. After this course the students will have refreshed their knowledge of probability theory and statistics to model uncertainties in view of engineering applications. They will be able to analyze the reliability of a structure and to use risk assessment methods for decision making under uncertain conditions. They will be aware of the state-of-the-art computational methods and software in this field.
ContentEngineers are confronted every day to decision making under limited amount of information and uncertain conditions. When designing new structures and systems, the design codes such as SIA or Euro- codes usually provide a framework that guarantees safety and reliability. However the level of safety is not quantified explicitly, which does not allow the analyst to properly choose between design variants and evaluate a total cost in case of failure. In contrast, the framework of risk analysis allows one to incorporate the uncertainty in decision making.

The first part of the course is a reminder on probability theory that is used as a main tool for reliability and risk analysis. Classical concepts such as random variables and vectors, dependence and correlation are recalled. Basic statistical inference methods used for building a probabilistic model from the available data, e.g. the maximum likelihood method, are presented.

The second part is related to structural reliability analysis, i.e. methods that allow one to compute probabilities of failure of a given system with respect to prescribed criteria. The framework of reliability analysis is first set up. Reliability indices are introduced together with the first order-second moment method (FOSM) and the first order reliability method (FORM). Methods based on Monte Carlo simulation are then reviewed and illustrated through various examples. By-products of reliability analysis such as sensitivity measures and partial safety coefficients are derived and their links to structural design codes is shown. The reliability of structural systems is also introduced as well as the methods used to reassess existing structures based on new information.

The third part of the course addresses risk assessment methods. Techniques for the identification of hazard scenarios and their representation by fault trees and event trees are described. Risk is defined with respect to the concept of expected utility in the framework of decision making. Elements of Bayesian decision making, i.e. pre-, post and pre-post risk assessment methods are presented.

The course also includes a tutorial using the UQLab software dedicated to real world structural reliability analysis.
Lecture notesSlides of the lectures are available online every week. A printed version of the full set of slides is proposed to the students at the beginning of the semester.
LiteratureAng, A. and Tang, W.H, Probability Concepts in Engineering - Emphasis on Applications to Civil and Environmental Engineering, 2nd Edition, John Wiley & Sons, 2007.

S. Marelli, R. Schöbi, B. Sudret, UQLab user manual - Structural reliability (rare events estimation), Report UQLab-V0.92-107.
Prerequisites / NoticeBasic course on probability theory and statistics
103-0307-00LMulti-Criteria Decision Analysis Information W3 credits2GA. Grêt-Regamey
AbstractPlanners need to make decisions about the best possible mix of land uses. With increasing availability of spatial databases and the analytical capabilities of GIS, more effective decision support systems can be developed. The goal of the course is to provide the basics of spatial analysis and to teach the integration of spatial data into multicriteria decision-making systems.
ObjectiveThis course will:
1) introduce students to techniques and issues associated with spatial modeling and decision support systems, including analytical techniques that are unique to spatial analysis
2) provide hands-on training in the use of these spatial tools in R while addressing real planning problems.

The emphasis is on concepts, resources, and analysis tools that students can use in science, private companies and government careers.
Lecture notes- Handouts of the lectures
- Script
- Exercise material

Download: Link
Prerequisites / NoticeThe course will presume basic knowledge of the R software package. RE&IS Master students will acquire this knowledge during the
"Basics of RE&IS" (103-0377-10L) course. Provided there are still available places, students from other disciplines can also join the part of "Basics of RE&IS" in which R is taught (i.e. first five lectures; no credit points will be awarded). These students can register for "Basics of RE&IS" by e-mailing Maarten van Strien (Link). Alternatively, they can acquire basic R knowledge with online tutorials, such as "Introduction to R" by W. N. Venables and D. M. Smith available online at Link.
Major Courses for all Majors
NumberTitleTypeECTSHoursLecturers
101-0439-00LIntroduction to Economic Analysis - A Case Study Approach with Cost Benefit Analysis in Transport
Remark:
Former Title "Introduction to Economic Policy - A Case Study Approach with Cost Benefit Analysis in Transport".
W6 credits4GK. W. Axhausen, R. Schubert
AbstractThe course presents basic economic principles as well as cost benefit analyses in transport; it also introduces methods used to derive the monetary values of non-market goods.
ObjectiveFamiliarity with basic microeconomic and macroeconomic principles and with the essential methods of project appraisal
ContentBasic microeconomic and macroeconomic üpronciples; Cost-Benefit-Analyses; multi-criteria analyses; European guidelines; stated response methods; travel cost approach and others; Valuation of travel time savings; valuation of traffic safety
Lecture notesmoodle platform for the basic economic principles; handouts
LiteratureTaylor, M.P., Mankiw, N.G. (2014): Economics; Harvard Press

VSS (2006) SN 640 820: Kosten-Nutzen-Analysen im Strassenverkehr, VSS, Zürich.

Boardman, A.E., D.H. Greenberg, A.R. Vining und D.L. Weimer (2001) Cost – Benefit – Analysis: Concepts and Practise, Prentice-Hall, Upper Saddle River.

ecoplan and metron (2005) Kosten-Nutzen-Analysen im Strassenverkehr: Kommentar zu SN 640 820, UVEK, Bern.
Electives
The entire course programs of ETH Zurich and Universitiy Zurich are open to the students to individual selection. The students have themselves to check whether they meet the admission requirements for a course.
Recommended Electives of Master Degree Programme
Students having enroled for 851-0703-03 earlier (i.e. bachelor's degree programme or as additional requirement for master's degree programme) cannot enrol for this again during master's degree programme.
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
406-0242-AALAnalysis II Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-7 credits15RM. Akka Ginosar
AbstractMathematical tools of an engineer
ObjectiveMathematics as a tool to solve engineering problems, mathematical formulation of problems in science and engineering. Basic mathematical knowledge of an engineers.
ContentMulti variable calculus: gradient, directional derivative, chain rule, Taylor expansion, Lagrange multipliers. Multiple integrals: coordinate transformations, path integrals, integrals over surfaces, divergence theorem, applications in physics. Ordinary differential equations.
LiteratureTextbooks in English:
- J. Stewart: Multivariable Calculus, Thomson Brooks/Cole
- V. I. Smirnov: A course of higher mathematics. Vol. II. Advanced calculus
- W. L. Briggs, L. Cochran: Calculus: Early Transcendentals: International Edition, Pearson Education

- M. Akveld, R. Sperb, Analysis II, vdf
- L. Papula: Mathematik für Ingenieure 2, Vieweg Verlag
Computational Science and Engineering Bachelor Information
First Year Compulsory Courses
First Year Examination Block 2
NumberTitleTypeECTSHoursLecturers
401-0231-10LAnalysis IO8 credits4V + 3UT. H. Willwacher
AbstractCalculus of one variable: Real and complex numbers, vectors, limits, sequences, series, power series, continuous maps, differentiation and integration in one variable, introduction to ordinary differential equations
ObjectiveEinfuehrung in die Grundlagen der Analysis
Lecture notesKonrad Koenigsberger, Analysis I.
Christian Blatter: Ingenieur-Analysis (Kapitel 1-3)
Basic Courses
Block G1
NumberTitleTypeECTSHoursLecturers
401-0353-00LAnalysis III Information O4 credits2V + 1UA. Figalli
AbstractIn this lecture we treat problems in applied analysis. The focus lies on the simplest cases of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation and the wave equation.
Objective
Content1.) Klassifizierung von PDE's
- linear, quasilinear, nicht-linear
- elliptisch, parabolisch, hyperbolisch

2.) Quasilineare PDE
- Methode der Charakteristiken (Beispiele)

3.) Elliptische PDE
- Bsp: Laplace-Gleichung
- Harmonische Funktionen, Maximumsprinzip, Mittelwerts-Formel.
- Methode der Variablenseparation.

4.) Parabolische PDE
- Bsp: Wärmeleitungsgleichung
- Bsp: Inverse Wärmeleitungsgleichung
- Methode der Variablenseparation

5.) Hyperbolische PDE
- Bsp: Wellengleichung
- Formel von d'Alembert in (1+1)-Dimensionen
- Methode der Variablenseparation

6.) Green'sche Funktionen
- Rechnen mit der Dirac-Deltafunktion
- Idee der Green'schen Funktionen (Beispiele)

7.) Ausblick auf numerische Methoden
- 5-Punkt-Diskretisierung des Laplace-Operators (Beispiele)
LiteratureY. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005)

Zusätzliche Literatur:
Erwin Kreyszig, "Advanced Engineering Mathematics", John Wiley & Sons, Kap. 8, 11, 16 (sehr gutes Buch, als Referenz zu benutzen)
Norbert Hungerbühler, "Einführung in die partiellen Differentialgleichungen", vdf Hochschulverlag AG an der ETH Zürich.
G. Felder:Partielle Differenzialgleichungen.
Link
Prerequisites / NoticePrerequisites: Analysis I and II, Fourier series (Komplexe Analysis)
Fields of Specialization
Computational Finance
NumberTitleTypeECTSHoursLecturers
401-4657-00LNumerical Analysis of Stochastic Ordinary Differential Equations Information
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
W6 credits3V + 1UA. Jentzen
AbstractCourse on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.
ObjectiveThe aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.
ContentGeneration of random numbers
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Multilevel Monte Carlo methods for SODEs
Applications to computational finance: Option valuation
Lecture notesLecture Notes are available in the lecture homepage (please follow the link in the Learning materials section).
LiteratureP. Glassermann:
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.

P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
Prerequisites / NoticePrerequisites:

Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.

a) mandatory courses:
Elementary Probability,
Probability Theory I.

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday, September 20, 2017

Date of the End-of-Semester examination: Wednesday, December 20, 2017, 13:00-15:00; students must arrive before 12:30 at ETH HG E 19.
Room for the End-of-Semester examination: ETH HG E 19.

Exam inspection: Monday, March 5, 2018,
13:00-14:00 at HG D 5.1
Please bring your legi.
Electives
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
401-4623-00LTime Series Analysis
Does not take place this semester.
W6 credits3Gnot available
AbstractStatistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R.
ObjectiveUnderstanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.
ContentThis course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations.
Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R.
Lecture notesNot available
LiteratureA list of references will be distributed during the course.
Prerequisites / NoticeBasic knowledge in probability and statistics
Computational Science and Engineering Master Information
Fields of Specialization
Computational Finance
NumberTitleTypeECTSHoursLecturers
401-4657-00LNumerical Analysis of Stochastic Ordinary Differential Equations Information
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
W6 credits3V + 1UA. Jentzen
AbstractCourse on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.
ObjectiveThe aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.
ContentGeneration of random numbers
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Multilevel Monte Carlo methods for SODEs
Applications to computational finance: Option valuation
Lecture notesLecture Notes are available in the lecture homepage (please follow the link in the Learning materials section).
LiteratureP. Glassermann:
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.

P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
Prerequisites / NoticePrerequisites:

Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.

a) mandatory courses:
Elementary Probability,
Probability Theory I.

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday, September 20, 2017

Date of the End-of-Semester examination: Wednesday, December 20, 2017, 13:00-15:00; students must arrive before 12:30 at ETH HG E 19.
Room for the End-of-Semester examination: ETH HG E 19.

Exam inspection: Monday, March 5, 2018,
13:00-14:00 at HG D 5.1
Please bring your legi.
Electives
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
401-4623-00LTime Series Analysis
Does not take place this semester.
W6 credits3Gnot available
AbstractStatistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R.
ObjectiveUnderstanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.
ContentThis course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations.
Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R.
Lecture notesNot available
LiteratureA list of references will be distributed during the course.
Prerequisites / NoticeBasic knowledge in probability and statistics
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
406-0353-AALAnalysis III Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-4 credits9RF. Da Lio
AbstractIntroduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics.
ObjectiveMathematical treatment of problems in science and engineering. To understand the properties of the different types of partlial differentail equations.
ContentLaplace Transforms:
- Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting
- Transforms of Derivatives and Integrals, ODEs
- Unit Step Function, t-Shifting
- Short Impulses, Dirac's Delta Function, Partial Fractions
- Convolution, Integral Equations
- Differentiation and Integration of Transforms

Fourier Series, Integrals and Transforms:
- Fourier Series
- Functions of Any Period p=2L
- Even and Odd Functions, Half-Range Expansions
- Forced Oscillations
- Approximation by Trigonometric Polynomials
- Fourier Integral
- Fourier Cosine and Sine Transform

Partial Differential Equations:
- Basic Concepts
- Modeling: Vibrating String, Wave Equation
- Solution by separation of variables; use of Fourier series
- D'Alembert Solution of Wave Equation, Characteristics
- Heat Equation: Solution by Fourier Series
- Heat Equation: Solutions by Fourier Integrals and Transforms
- Modeling Membrane: Two Dimensional Wave Equation
- Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series
- Solution of PDEs by Laplace Transform
LiteratureE. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011

C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed.
Stanley J. Farlow, Partial Differential Equations for Scientists and Engineers, (Dover Books on Mathematics).

G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003.

Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005

For reference/complement of the Analysis I/II courses:

Christian Blatter: Ingenieur-Analysis (Download PDF)
Prerequisites / NoticeUp-to-date information about this course can be found at:
Link
Robotics, Systems and Control Master Information
Core Courses
NumberTitleTypeECTSHoursLecturers
227-0447-00LImage Analysis and Computer Vision Information W6 credits3V + 1UL. Van Gool, O. Göksel, E. Konukoglu
AbstractLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation and deformable shape matching. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition.
ObjectiveOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
ContentThe first part of the course starts off from an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First it is investigated how the parameters of the electromagnetic waves are related to our perception. Also the interaction of light with matter is considered. The most important hardware components of technical vision systems, such as cameras, optical devices and illumination sources are discussed. The course then turns to the steps that are necessary to arrive at the discrete images that serve as input to algorithms. The next part describes necessary preprocessing steps of image analysis, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and depth as two important examples. The estimation of image velocities (optical flow) will get due attention and methods for object tracking will be presented. Several techniques are discussed to extract three-dimensional information about objects and scenes. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed.
Lecture notesCourse material Script, computer demonstrations, exercises and problem solutions
Prerequisites / NoticePrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Linux and C.
The course language is English.
227-0526-00LPower System Analysis Information W6 credits4GG. Hug
AbstractThe goal of this course is understanding the stationary and dynamic problems in electrical power systems. The course includes the development of stationary models of the electrical network, their mathematical representation and special characteristics and solution methods of large linear and non-linear systems of equations related to electrical power networks.
ObjectiveThe goal of this course is understanding the stationary and dynamic problems in electrical power systems and the application of analysis tools in steady and dynamic states.
ContentThe course includes the development of stationary models of the electrical network, their mathematical representation and special characteristics and solution methods of large linear and non-linear systems of equations related to electrical power grids. Approaches such as the Newton-Raphson algorithm applied to power flow equations, superposition technique for short-circuit analysis, equal area criterion and nose curve analysis are discussed as well as power flow computation techniques for distribution grids.
Lecture notesLecture notes.
Science, Technology, and Policy Master Information
Core Courses
NumberTitleTypeECTSHoursLecturers
860-0002-00LQuantitative Policy Analysis and ModelingO6 credits4GA. Patt, T. Schmidt, E. Trutnevyte, O. van Vliet
AbstractThe lectures will introduce students to the principles of quantitative policy analysis, namely the methods to predict and evaluate the social, economic, and environmental effects of alternative strategies to achieve public objectives. A series of graded assignments will give students an opportunity for students to apply those methods to a set of case studies
ObjectiveThe objectives of this course are to develop the following key skills necessary for policy analysts:
- Identifying the critical quantitative factors that are of importance to policy makers in a range of decision-making situations.
- Developing conceptual models of the types of processes and relationships governing these quantitative factors, including stock-flow dynamics, feedback loops, optimization, sources and effects of uncertainty, and agent coordination problems.
- Develop and program numerical models to simulate the processes and relationships, in order to identify policy problems and the effects of policy interventions.
- Communicate the findings from these simulations and associated analysis in a manner that makes transparent their theoretical foundation, the level and sources of uncertainty, and ultimately their applicability to the policy problem.
The course will proceed through a series of policy analysis and modeling exercises, involving real-world or hypothetical problems. The specific examples around which work will be done will concern the environment, energy, health, and natural hazards management.
Electives
NumberTitleTypeECTSHoursLecturers
101-0439-00LIntroduction to Economic Analysis - A Case Study Approach with Cost Benefit Analysis in Transport
Remark:
Former Title "Introduction to Economic Policy - A Case Study Approach with Cost Benefit Analysis in Transport".
W6 credits4GK. W. Axhausen, R. Schubert
AbstractThe course presents basic economic principles as well as cost benefit analyses in transport; it also introduces methods used to derive the monetary values of non-market goods.
ObjectiveFamiliarity with basic microeconomic and macroeconomic principles and with the essential methods of project appraisal
ContentBasic microeconomic and macroeconomic üpronciples; Cost-Benefit-Analyses; multi-criteria analyses; European guidelines; stated response methods; travel cost approach and others; Valuation of travel time savings; valuation of traffic safety
Lecture notesmoodle platform for the basic economic principles; handouts
LiteratureTaylor, M.P., Mankiw, N.G. (2014): Economics; Harvard Press

VSS (2006) SN 640 820: Kosten-Nutzen-Analysen im Strassenverkehr, VSS, Zürich.

Boardman, A.E., D.H. Greenberg, A.R. Vining und D.L. Weimer (2001) Cost – Benefit – Analysis: Concepts and Practise, Prentice-Hall, Upper Saddle River.

ecoplan and metron (2005) Kosten-Nutzen-Analysen im Strassenverkehr: Kommentar zu SN 640 820, UVEK, Bern.
Sport Teaching Diploma Information
Detailed information on the programme at: Link
Additional Requirements in Sports Science
NumberTitleTypeECTSHoursLecturers
376-2019-00LApplied Movement Analysis Information W2 credits2GR. Scharpf, S. Lorenzetti
AbstractBased on practical examples out of sport, everyday movement and therapy, students use and compare different methods of movement analysis.
ObjectiveStudents are able to assess human movement using different methods of movement analysis.
ContentDuring the course students get acquainted with different methods of movement analysis such as: functional, morphological, clinical, mechanical, and others.
Based on practical examples, these methods are used and compared. The examples range from sport, everyday movement and therapy, such as hockey, gymnastics, acrobatics, badminton, gait / running and strength training. In the first phase of the class, the different approaches are applied. In the second phase, small teams are working on individual projects. These will be discussed and presented in plenum.
Lecture notesClass material will be distributed using the moodle platform.
Statistics Master Information
The following courses belong to the curriculum of the Master's Programme in Statistics. The corresponding credits do not count as external credits even for course units where an enrolment at ETH Zurich is not possible.
Core Courses
In each subject area, the core courses offered are normally mathematical as well as application-oriented in content. For each subject area, only one of these is recognised for the Master degree.
Analysis of Variance and Design of Experiments
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
Time Series and Stochastic Processes
NumberTitleTypeECTSHoursLecturers
401-4623-00LTime Series Analysis
Does not take place this semester.
W6 credits3Gnot available
AbstractStatistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R.
ObjectiveUnderstanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R.
ContentThis course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations.
Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations,
spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R.
Lecture notesNot available
LiteratureA list of references will be distributed during the course.
Prerequisites / NoticeBasic knowledge in probability and statistics
Specialization Areas and Electives
Statistical and Mathematical Courses
NumberTitleTypeECTSHoursLecturers
401-6217-00LUsing R for Data Analysis and Graphics (Part II) Information W1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the second part an introduction to the statistical software R for scientists. Topics are data generation and selection, graphical functions, important statistical functions, types of objects, models, programming and writing functions.
Note: This part builds on "Using R... (Part I)", but can be taken independently if the basics of R are already known.
ObjectiveThe students will be able to use the software R efficiently for data analysis.
ContentThe course provides the second part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part II of the course builds on part I and covers the following additional topics:
- Elements of the R language: control structures (if, else, loops), lists, overview of R objects, attributes of R objects;
- More on R functions;
- Applying functions to elements of vectors, matrices and lists;
- Object oriented programming with R: classes and methods;
- Tayloring R: options
- Extending basic R: packages

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeBasic knowledge of R equivalent to "Using R .. (part 1)" ( = 401-6215-00L ) is a prerequisite for this course.

The course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
401-6282-00LStatistical Analysis of High-Throughput Genomic and Transcriptomic Data (University of Zurich)
No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH.
UZH Module Code: STA426

Mind the enrolment deadlines at UZH:
Link
W5 credits3GH. Rehrauer, M. Robinson
AbstractA range of topics will be covered, including basic molecular biology, genomics technologies and in particular, a wide range of statistical and computational methods that have been used in the analysis of DNA microarray and high throughput sequencing experiments.
Objective-Understand the fundamental "scientific process" in the field of Statistical Bioinformatics
-Be equipped with the skills/tools to preprocess genomic data (Unix, Bioconductor, mapping, etc.) and ensure reproducible research (Sweave)
-Have a general knowledge of the types of data and biological applications encountered with microarray and sequencing data
-Have the general knowledge of the range of statistical methods that get used with microarray and sequencing data
-Gain the ability to apply statistical methods/knowledge/software to a collaborative biological project
-Gain the ability to critical assess the statistical bioinformatics literature
-Write a coherent summary of a bioinformatics problem and its solution in statistical terms
ContentLectures will include: microarray preprocessing; normalization; exploratory data analysis techniques such as clustering, PCA and multidimensional scaling; Controlling error rates of statistical tests (FPR versus FDR versus FWER); limma (linear models for microarray analysis); mapping algorithms (for RNA/ChIP-seq); RNA-seq quantification; statistical analyses for differential count data; isoform switching; epigenomics data including DNA methylation; gene set analyses; classification
Lecture notesLecture notes, published manuscripts
Prerequisites / NoticePrerequisites: Basic knowlegde of the programming language R, sufficient knowledge in statistics

Former course title: Statistical Methods for the Analysis of Microarray and Short-Read Sequencing Data
Statistical and Mathematical Courses: not eligible for credits
NumberTitleTypeECTSHoursLecturers
401-6215-00LUsing R for Data Analysis and Graphics (Part I) Information E-1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the first part an introduction to the statistical software R for scientists. Topics covered are data generation and selection, graphical and basic statistical functions, creating simple functions, basic types of objects.
ObjectiveThe students will be able to use the software R for simple data analysis.
ContentThe course provides the first part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part I of the course covers the following topics:
- What is R?
- R Basics: reading and writing data from/to files, creating vectors & matrices, selecting elements of dataframes, vectors and matrices, arithmetics;
- Types of data: numeric, character, logical and categorical data, missing values;
- Simple (statistical) functions: summary, mean, var, etc., simple statistical tests;
- Writing simple functions;
- Introduction to graphics: scatter-, boxplots and other high-level plotting functions, embellishing plots by title, axis labels, etc., adding elements (lines, points) to existing plots.

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link

Note: Part I of UsingR is complemented and extended by Part II, which is offered during the second part of the semester and which can be taken independently from Part I.
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeThe course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
Environmental Engineering Bachelor Information
1. Semester
First Year Examinations (1. Sem.)
NumberTitleTypeECTSHoursLecturers
401-0241-00LAnalysis I Information O7 credits5V + 2UM. Akka Ginosar
AbstractMathematical tools for the engineer
ObjectiveMathematics as a tool to solve engineering problems. Mathematical formulation of technical and scientific problems. Basic mathematical knowledge for engineers.
ContentComplex numbers.
Calculus for functions of one variable with applications.
Simple Mathematical models in engineering.
Lecture notesDie Vorlesung folgt weitgehend

Klaus Dürrschnabel, "Mathematik für Ingenieure - Eine Einführung mit Anwendungs- und Alltagsbeispielen", Springer; online verfügbar unter:
Link
LiteratureNeben Klaus Dürrschnabel, "Mathematik für Ingenieure - Eine Einführung mit Anwendungs- und Alltagsbeispielen", Springer sind auch die folgenden Bücher/Skripte empfehlenswert und decken den zu behandelnden Stoff ab:

Tilo Arens et al., "Mathematik", Springer; online verfügbar unter:
Link

Meike Akveld, "Analysis 1", vdf;
Link

Urs Stammbach, "Analysis I/II" (erhältlich im ETH Store);
Link
5. Semester
Elective Blocks
Elective Block: Energy
NumberTitleTypeECTSHoursLecturers
227-1631-00LEnergy System Analysis Information W4 credits3GG. Hug, S. Hellweg, F. Noembrini, A. Schlüter
AbstractThe course provides an introduction to the methods and tools for analysis of energy consumption, energy production and energy flows. Environmental aspects are included as well as economical considerations. Different sectors of the society are discussed, such as electric power, buildings, and transportation. Models for energy system analysis planning are introduced.
ObjectiveThe purpose of the course is to give the participants an overview of the methods and tools used for energy systems analysis and how to use these in simple practical examples.
ContentThe course gives an introduction to methods and tools for analysis of energy consumption, energy production and energy flows. Both larger systems, e.g. countries, and smaller systems, e.g. industries, homes, vehicles, are studied. The tools and methods are applied to various problems during the exercises. Different conventions of energy statistics used are introduced.

The course provides also an introduction to energy systems models for developing scenarios of future energy consumption and production. Bottom-up and Top-Down approaches are addressed and their features and applications discussed.

The course contains the following parts:
Part I: Energy flows and energy statistics
Part II: Environmental impacts
Part III: Electric power systems
Part IV: Energy in buildings
Part V: Energy in transportation
Part VI: Energy systems models
Lecture notesHandouts
LiteratureExcerpts from various books, e.g. K. Blok: Introduction to Energy Analysis, Techne Press, Amsterdam 2006, ISBN 90-8594-016-8
Environmental Engineering Master Information
Master Studies (Programme Regulations 2016)
Majors
Major Urban Water Management
Compulsory Moudules
System Analysis in Urban Water Management
NumberTitleTypeECTSHoursLecturers
102-0227-00LSystems Analysis and Mathematical Modeling in Urban Water Management Information O6 credits4GE. Morgenroth, M. Maurer
AbstractSystematic introduction of material balances, transport processes, kinetics, stoichiometry and conservation. Ideal reactors, residence time distribution, heterogeneous systems, dynamic response of reactors. Parameter identification, local sensitivity, error propagation, Monte Carlo simulation. Introduction to real time control (PID controllers). Extensive coding of examples in Berkeley Madonna.
ObjectiveThe goal of this course is to provide the students with an understanding and the tools to develop their own mathematical models, to plan experiments, to evaluate error propagation and to test simple process control strategies in the field of process engineering in urban water management.
ContentThe course will provide a broad introduction into the fundamentals of modeling water treatment systems. The topics are:
- Introduction into modeling and simulation
- The material balance equations, transport processes, transformation processes (kinetics, stoichiometry, conservation)
- Ideal reactors
- Hydraulic residence time distribution and modeling of real reactors
- Dynamic behavior of reactor systems
- Systems analytical tools: Sensitivity, parameter identification, error propagation, Monte Carlo simulation
- Introduction to process control (PID controller, fuzzy control)
Lecture notesCopies of overheads will be made available.
LiteratureThere will be a required textbook that students need to purchase:
Willi Gujer (2008): Systems Analysis for Water Technology. Springer-Verlag, Berlin Heidelberg
Prerequisites / NoticeThis course will be offered together with the course Process Engineering Ia. It is advantageous to follow both courses simultaneously.
Major Environmental Technologies
Compulsory Moudules
System Analysis in Urban Water Management
Note: Students taking both of the modules WASTE and SysUMW must take the course 102-0337-00 Landfilling, Contaminated Sites and Radioactive Waste Repositories in module WASTE as replacement for 102-0217-00 Process Engineering Ia being listed in both modules.
NumberTitleTypeECTSHoursLecturers
102-0227-00LSystems Analysis and Mathematical Modeling in Urban Water Management Information O6 credits4GE. Morgenroth, M. Maurer
AbstractSystematic introduction of material balances, transport processes, kinetics, stoichiometry and conservation. Ideal reactors, residence time distribution, heterogeneous systems, dynamic response of reactors. Parameter identification, local sensitivity, error propagation, Monte Carlo simulation. Introduction to real time control (PID controllers). Extensive coding of examples in Berkeley Madonna.
ObjectiveThe goal of this course is to provide the students with an understanding and the tools to develop their own mathematical models, to plan experiments, to evaluate error propagation and to test simple process control strategies in the field of process engineering in urban water management.
ContentThe course will provide a broad introduction into the fundamentals of modeling water treatment systems. The topics are:
- Introduction into modeling and simulation
- The material balance equations, transport processes, transformation processes (kinetics, stoichiometry, conservation)
- Ideal reactors
- Hydraulic residence time distribution and modeling of real reactors
- Dynamic behavior of reactor systems
- Systems analytical tools: Sensitivity, parameter identification, error propagation, Monte Carlo simulation
- Introduction to process control (PID controller, fuzzy control)
Lecture notesCopies of overheads will be made available.
LiteratureThere will be a required textbook that students need to purchase:
Willi Gujer (2008): Systems Analysis for Water Technology. Springer-Verlag, Berlin Heidelberg
Prerequisites / NoticeThis course will be offered together with the course Process Engineering Ia. It is advantageous to follow both courses simultaneously.
Elective Modules
For all majors.
EM: System Analysis in Urban Water Management
Elective Module for Majors "Resource Management", "River and Hydraulic Engineering" and "Water Resources Management".

Note: Students taking both of the modules WASTE and SysUMW must take the course 102-0337-00 Landfilling, Contaminated Sites and Radioactive Waste Repositories in module WASTE as replacement for 102-0217-00 Process Engineering Ia being listed in both modules.
NumberTitleTypeECTSHoursLecturers
102-0227-00LSystems Analysis and Mathematical Modeling in Urban Water Management Information W6 credits4GE. Morgenroth, M. Maurer
AbstractSystematic introduction of material balances, transport processes, kinetics, stoichiometry and conservation. Ideal reactors, residence time distribution, heterogeneous systems, dynamic response of reactors. Parameter identification, local sensitivity, error propagation, Monte Carlo simulation. Introduction to real time control (PID controllers). Extensive coding of examples in Berkeley Madonna.
ObjectiveThe goal of this course is to provide the students with an understanding and the tools to develop their own mathematical models, to plan experiments, to evaluate error propagation and to test simple process control strategies in the field of process engineering in urban water management.
ContentThe course will provide a broad introduction into the fundamentals of modeling water treatment systems. The topics are:
- Introduction into modeling and simulation
- The material balance equations, transport processes, transformation processes (kinetics, stoichiometry, conservation)
- Ideal reactors
- Hydraulic residence time distribution and modeling of real reactors
- Dynamic behavior of reactor systems
- Systems analytical tools: Sensitivity, parameter identification, error propagation, Monte Carlo simulation
- Introduction to process control (PID controller, fuzzy control)
Lecture notesCopies of overheads will be made available.
LiteratureThere will be a required textbook that students need to purchase:
Willi Gujer (2008): Systems Analysis for Water Technology. Springer-Verlag, Berlin Heidelberg
Prerequisites / NoticeThis course will be offered together with the course Process Engineering Ia. It is advantageous to follow both courses simultaneously.
Master Studies (Programme Regulations 2006)
Major Courses
Major in Urban Water Management
NumberTitleTypeECTSHoursLecturers
102-0227-00LSystems Analysis and Mathematical Modeling in Urban Water Management Information O6 credits4GE. Morgenroth, M. Maurer
AbstractSystematic introduction of material balances, transport processes, kinetics, stoichiometry and conservation. Ideal reactors, residence time distribution, heterogeneous systems, dynamic response of reactors. Parameter identification, local sensitivity, error propagation, Monte Carlo simulation. Introduction to real time control (PID controllers). Extensive coding of examples in Berkeley Madonna.
ObjectiveThe goal of this course is to provide the students with an understanding and the tools to develop their own mathematical models, to plan experiments, to evaluate error propagation and to test simple process control strategies in the field of process engineering in urban water management.
ContentThe course will provide a broad introduction into the fundamentals of modeling water treatment systems. The topics are:
- Introduction into modeling and simulation
- The material balance equations, transport processes, transformation processes (kinetics, stoichiometry, conservation)
- Ideal reactors
- Hydraulic residence time distribution and modeling of real reactors
- Dynamic behavior of reactor systems
- Systems analytical tools: Sensitivity, parameter identification, error propagation, Monte Carlo simulation
- Introduction to process control (PID controller, fuzzy control)
Lecture notesCopies of overheads will be made available.
LiteratureThere will be a required textbook that students need to purchase:
Willi Gujer (2008): Systems Analysis for Water Technology. Springer-Verlag, Berlin Heidelberg
Prerequisites / NoticeThis course will be offered together with the course Process Engineering Ia. It is advantageous to follow both courses simultaneously.
Minors
NumberTitleTypeECTSHoursLecturers
102-0227-00LSystems Analysis and Mathematical Modeling in Urban Water Management Information W6 credits4GE. Morgenroth, M. Maurer
AbstractSystematic introduction of material balances, transport processes, kinetics, stoichiometry and conservation. Ideal reactors, residence time distribution, heterogeneous systems, dynamic response of reactors. Parameter identification, local sensitivity, error propagation, Monte Carlo simulation. Introduction to real time control (PID controllers). Extensive coding of examples in Berkeley Madonna.
ObjectiveThe goal of this course is to provide the students with an understanding and the tools to develop their own mathematical models, to plan experiments, to evaluate error propagation and to test simple process control strategies in the field of process engineering in urban water management.
ContentThe course will provide a broad introduction into the fundamentals of modeling water treatment systems. The topics are:
- Introduction into modeling and simulation
- The material balance equations, transport processes, transformation processes (kinetics, stoichiometry, conservation)
- Ideal reactors
- Hydraulic residence time distribution and modeling of real reactors
- Dynamic behavior of reactor systems
- Systems analytical tools: Sensitivity, parameter identification, error propagation, Monte Carlo simulation
- Introduction to process control (PID controller, fuzzy control)
Lecture notesCopies of overheads will be made available.
LiteratureThere will be a required textbook that students need to purchase:
Willi Gujer (2008): Systems Analysis for Water Technology. Springer-Verlag, Berlin Heidelberg
Prerequisites / NoticeThis course will be offered together with the course Process Engineering Ia. It is advantageous to follow both courses simultaneously.
101-0187-00LStructural Reliability and Risk Analysis Information W3 credits2GS. Marelli
AbstractStructural reliability aims at quantifying the probability of failure of systems due to uncertainties in their design, manufacturing and environmental conditions. Risk analysis combines this information with the consequences of failure in view of optimal decision making. The course presents the underlying probabilistic modelling and computational methods for reliability and risk assessment.
ObjectiveThe goal of this course is to provide the students with a thorough understanding of the key concepts behind structural reliability and risk analysis. After this course the students will have refreshed their knowledge of probability theory and statistics to model uncertainties in view of engineering applications. They will be able to analyze the reliability of a structure and to use risk assessment methods for decision making under uncertain conditions. They will be aware of the state-of-the-art computational methods and software in this field.
ContentEngineers are confronted every day to decision making under limited amount of information and uncertain conditions. When designing new structures and systems, the design codes such as SIA or Euro- codes usually provide a framework that guarantees safety and reliability. However the level of safety is not quantified explicitly, which does not allow the analyst to properly choose between design variants and evaluate a total cost in case of failure. In contrast, the framework of risk analysis allows one to incorporate the uncertainty in decision making.

The first part of the course is a reminder on probability theory that is used as a main tool for reliability and risk analysis. Classical concepts such as random variables and vectors, dependence and correlation are recalled. Basic statistical inference methods used for building a probabilistic model from the available data, e.g. the maximum likelihood method, are presented.

The second part is related to structural reliability analysis, i.e. methods that allow one to compute probabilities of failure of a given system with respect to prescribed criteria. The framework of reliability analysis is first set up. Reliability indices are introduced together with the first order-second moment method (FOSM) and the first order reliability method (FORM). Methods based on Monte Carlo simulation are then reviewed and illustrated through various examples. By-products of reliability analysis such as sensitivity measures and partial safety coefficients are derived and their links to structural design codes is shown. The reliability of structural systems is also introduced as well as the methods used to reassess existing structures based on new information.

The third part of the course addresses risk assessment methods. Techniques for the identification of hazard scenarios and their representation by fault trees and event trees are described. Risk is defined with respect to the concept of expected utility in the framework of decision making. Elements of Bayesian decision making, i.e. pre-, post and pre-post risk assessment methods are presented.

The course also includes a tutorial using the UQLab software dedicated to real world structural reliability analysis.
Lecture notesSlides of the lectures are available online every week. A printed version of the full set of slides is proposed to the students at the beginning of the semester.
LiteratureAng, A. and Tang, W.H, Probability Concepts in Engineering - Emphasis on Applications to Civil and Environmental Engineering, 2nd Edition, John Wiley & Sons, 2007.

S. Marelli, R. Schöbi, B. Sudret, UQLab user manual - Structural reliability (rare events estimation), Report UQLab-V0.92-107.
Prerequisites / NoticeBasic course on probability theory and statistics
Course Units for Additional Admission Requirements
The courses below are only available for MSc students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
102-0324-AALEcological Systems Analysis Information
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-6 credits4RS. Hellweg
AbstractMethodological basics and application of various environmental assessment tools.
ObjectiveStudents learn about environmental assessment tools, such as material flow analysis, risk assessment, and life cycle assessment. They can identify and apply the appropriate tool in a given situation. Also, they are able to critically assess existing studies.
Content- Methodological basics of material flow analysis, risk assessment and life cycle assessment
- Application of these methods to case studies
Lecture notesNo script, but literature available on homepage.
LiteratureLiterature available on
Link
Prerequisites / NoticeNone
Environmental Sciences Bachelor Information
Bachelor Studies (Programme Regulations 2016)
Basic Courses I
First Year Examinations
NumberTitleTypeECTSHoursLecturers
401-0251-00LMathematics IO6 credits4V + 2UL. Halbeisen
AbstractThis course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.
ObjectiveMathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment.

The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses.
Content1. Single-Variable Calculus:
review of differentiation, linearisation, Taylor polynomials, maxima and minima, antiderivative, fundamental theorem of calculus, integration methods, improper integrals.

2. Linear Algebra and Complex Numbers:
systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra.

3. Ordinary Differential Equations:
separable ordinary differential equations (ODEs), integration by substitution, 1st and 2nd order linear ODEs, homogeneous systems of linear ODEs with constant coefficients, introduction to 2-dimensional dynamical systems.
Literature- Thomas, G. B.: Thomas' Calculus, Part 1 (Pearson Addison-Wesley).
- Bretscher, O.: Linear Algebra with Applications (Pearson Prentice Hall).
Prerequisites / NoticePrerequisites: familiarity with the basic notions from Calculus, in particular those of function and derivative.

Mathe-Lab (Assistance):
Mondays 12-14, Tuesdays 17-19, Wednesdays 17-19, in Room HG E 41.
Basic Courses II
Examination Blocks
Examination Block 2
NumberTitleTypeECTSHoursLecturers
701-0071-00LMathematics III: Systems AnalysisO4 credits2V + 1UN. Gruber, M. Vogt
AbstractThe objective of the systems analysis course is to deepen and illustrate the mathematical concepts on the basis of a series of very concrete examples. Topics covered include: linear box models with one or several variables, non-linear box models with one or several variables, time-discrete models, and continuous models in time and space.
ObjectiveLearning and applying of concepts (models) and quantitative methods to address concrete problems of environmental relevance. Understanding and applying the systems-analytic approach, i.e., Recognizing the core of the problem - simplification - quantitative approach - prediction.
ContentLink
Lecture notesOverhead slides will be made available through Ilias.
LiteratureImboden, D.S. and S. Pfenninger (2013) Introduction to Systems Analysis: Mathematically Modeling Natural Systems. Berlin Heidelberg: Springer Verlag.

Link
Natural Science and Technical Electives
Methodes of Statistical Data Analysis
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
401-6215-00LUsing R for Data Analysis and Graphics (Part I) Information W1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the first part an introduction to the statistical software R for scientists. Topics covered are data generation and selection, graphical and basic statistical functions, creating simple functions, basic types of objects.
ObjectiveThe students will be able to use the software R for simple data analysis.
ContentThe course provides the first part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part I of the course covers the following topics:
- What is R?
- R Basics: reading and writing data from/to files, creating vectors & matrices, selecting elements of dataframes, vectors and matrices, arithmetics;
- Types of data: numeric, character, logical and categorical data, missing values;
- Simple (statistical) functions: summary, mean, var, etc., simple statistical tests;
- Writing simple functions;
- Introduction to graphics: scatter-, boxplots and other high-level plotting functions, embellishing plots by title, axis labels, etc., adding elements (lines, points) to existing plots.

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link

Note: Part I of UsingR is complemented and extended by Part II, which is offered during the second part of the semester and which can be taken independently from Part I.
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeThe course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
401-6217-00LUsing R for Data Analysis and Graphics (Part II) Information W1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the second part an introduction to the statistical software R for scientists. Topics are data generation and selection, graphical functions, important statistical functions, types of objects, models, programming and writing functions.
Note: This part builds on "Using R... (Part I)", but can be taken independently if the basics of R are already known.
ObjectiveThe students will be able to use the software R efficiently for data analysis.
ContentThe course provides the second part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part II of the course builds on part I and covers the following additional topics:
- Elements of the R language: control structures (if, else, loops), lists, overview of R objects, attributes of R objects;
- More on R functions;
- Applying functions to elements of vectors, matrices and lists;
- Object oriented programming with R: classes and methods;
- Tayloring R: options
- Extending basic R: packages

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeBasic knowledge of R equivalent to "Using R .. (part 1)" ( = 401-6215-00L ) is a prerequisite for this course.

The course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
Specialization in an Environmental System
Human-Environment Systems
NumberTitleTypeECTSHoursLecturers
701-0651-00LCoevolution between Society and Environment: Analysis and InfluenceW3 credits2VJ. Minsch
AbstractAnalysis of central mechanisms of the anthroposphere: ecological economics, theory of institutions and innovation, development economics.
ObjectiveIntroduction to the theoretical foundations of the analysis of central mechanisms of the anthroposphere – in a sustainable development perspective.

Knowledge of the different scientific and political discussions on sustainable development.

Knowledge of selected analytical tools (Ecological Economics, economic analysis of institutions, innovation theory, “Ordnungstheorie”, Theory of liberal economic policy).

Ability to identify central non sustainable mechanisms and policies, to formulate adequate research questions, to choose and to use adequate analytical tools, and to elaborate solutions.
ContentSustainable development-update: origins, conceptions, state of the discussion. What's left after 25 years of discussion?

Development as Freedom: Foundations of a human-rights-based Society and Economy (Amartya Sen, Daron Acemoglu / James A. Robinson, Ralf Dahrendorf, Friedrich. A. von Hayek, Karl. R. Popper. Walter Eucken).

Market Economy:
Its Critics, Reforms and new Developments.

An Inquiry into the Nature and Causes of ...Non-Sustainability:
Selected mechanisms and trends. The “neo-mercantilism-syndrom”

New Trends in the Growth Debate:
The Growth-spiral” (Hans Chr. Binswanger), Prosperity without growth? (T. Jackson), Intelligent Growth (R. Fücks)

The Internet of Things and Collaborative Commons - on the road to "The Zero Marginal Cost Society"?

Sufficiency: Perspectives of a resource-light society

Corporation 2020 - Transforming Business for Tomorrow's World (Remarks on Pavan Sukhdev's bestseller)

Finance Crash and Debt Crisis - new challenges for Democracy & Market Economy

Resourcecurse: Resources, democracy, and economic development

Globalization: Facts and elements of a fair globalization

It`s the software! Institutional Innovations for Sustainable Development. Let's continue writing The Federalist Papers!

On the way to the second "Great Transformation"

Perspectives for further, deeper analysis
Lecture notesskript and additional texts are distributed in the cource
LiteratureA first selection:
- Daron Acemoglu / James A. Robinson (2012): Why Nations Fail. The Origins of Power, Prosperity, and Poverty, New York
- Hans Christoph Binswanger (2006): Die Wachstumsspirale. Geld, Energie und Imagination in der Dynamik des Marksprozesses, Marburg
- Ralf Dahrendorf ( 2003): Auf der Suche nach einer neuen Ordnung, München
- Jared Diamond (2005): Collapse: How Societies Choose to Fail or Succeed, New York
- Ralf Fücks (2013): Intelligent wachsten, Die grüne Revolution, München
- Friedrich A. von Hayek (1991): Die Verfassung der Freiheit, 3. Auflage, Tübingen
- Friedrich A. von Hayek (1972): Theorie komplexer Phänomene, Tübingen
- Tim Jackson (2009): Prosperity without Growth. Economics for a Finite Planet, London
- Jürg Minsch / Peter H. Feindt / Hans. P. Meister / Uwe Schneidewind / Tobias Schulz (1998): Institutionelle Reformen für eine Politik der Nachhaltigkeit, Berlin / Heidelberg / New York
- J. Minsch / A. Eberle / B. Meier / U. Schneidewind (1996). Mut zum ökologischen Umbau. Innovationsstrategien für Unternehmen, Politik und Akteurnetze, Birkhäuser, Basel / Boston / Berlin
- Elinor Ostrom (1990): Governing the Commons, Cambridge University Press, Cambridge / New York / Melbourne
- oekom e.V., Hrsg. (2013): Baustelle Zukunft. die Grosse Trasformation von Wirtschaft und Gesellschaft, oekom Verlag, München
- Karl Polanyi (1944): The Great Transformation
- Karl. R. Popper (1980): Die offene Gesellschaft und ihre Feinde, Bde. I und II, 6. Auflage, Tübingen
Jeremy Rifkin (2014): The Zero Mrginal Cost Society: The Internet of things, the Collaborative Commons, and the Eclipse of Capitalism, palgrave macmillan
- Uwe Schneidewind / Angelika Zahrnt (2013): Damit gutes Leben einfacher wird. Perspektiven einer Suffizienzpolitik, München
- Pavan Sukhdev (2012): Corporation 2020. Transforming Business for Tomorrow's World, Washington D.C.
- Tomas Sedlacek (2012): Die Ökonomie von Gut und Böse, München
- Amartya Sen (1999): Development as Freedom, New York 1999)
- Daniel Spreng /Thomas Flüeler /David Goldblatt /Jürg Minsch (2012): Tackling Long Term Global Energy Problems: The Contribution of Social Science, Dortrecht / Heidelberg / New York
- Joseph Stiglitz (2006): Making Globalization Work, New York 2006)
- Peter Ulrich (2005): Zivilisierte Marktwirtschaft, 2. Aufl., Freiburg
- WBGU Wissenschaftlicher Beirat der Bundesregierung Globale Umweltveränderungen (2011): Welt im Wandel. Gesellschaftsvertrag für eine Grosse Transformation, Zusammenfassung für Entscheidungsträger, WBGU, Berlin, Link

Further reading and citations are listed in the skript and mentioned in the course.
Prerequisites / NoticeWillingness to prepare intensively the topics and to participate actively in the course
Bachelor Studies (Programme Regulations 2011)
Basic Courses II
Examination Blocks
Examination Block 2
NumberTitleTypeECTSHoursLecturers
701-0071-00LMathematics III: Systems AnalysisO4 credits2V + 1UN. Gruber, M. Vogt
AbstractThe objective of the systems analysis course is to deepen and illustrate the mathematical concepts on the basis of a series of very concrete examples. Topics covered include: linear box models with one or several variables, non-linear box models with one or several variables, time-discrete models, and continuous models in time and space.
ObjectiveLearning and applying of concepts (models) and quantitative methods to address concrete problems of environmental relevance. Understanding and applying the systems-analytic approach, i.e., Recognizing the core of the problem - simplification - quantitative approach - prediction.
ContentLink
Lecture notesOverhead slides will be made available through Ilias.
LiteratureImboden, D.S. and S. Pfenninger (2013) Introduction to Systems Analysis: Mathematically Modeling Natural Systems. Berlin Heidelberg: Springer Verlag.

Link
Natural Science and Technical Electives
Natural Science Modules
Methodes of Statistical Data Analysis
NumberTitleTypeECTSHoursLecturers
401-0625-01LApplied Analysis of Variance and Experimental Design Information W5 credits2V + 1UL. Meier
AbstractPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
ObjectiveParticipants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R.
ContentPrinciples of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power.
LiteratureG. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000.
Prerequisites / NoticeThe exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held.
401-6215-00LUsing R for Data Analysis and Graphics (Part I) Information W1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the first part an introduction to the statistical software R for scientists. Topics covered are data generation and selection, graphical and basic statistical functions, creating simple functions, basic types of objects.
ObjectiveThe students will be able to use the software R for simple data analysis.
ContentThe course provides the first part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part I of the course covers the following topics:
- What is R?
- R Basics: reading and writing data from/to files, creating vectors & matrices, selecting elements of dataframes, vectors and matrices, arithmetics;
- Types of data: numeric, character, logical and categorical data, missing values;
- Simple (statistical) functions: summary, mean, var, etc., simple statistical tests;
- Writing simple functions;
- Introduction to graphics: scatter-, boxplots and other high-level plotting functions, embellishing plots by title, axis labels, etc., adding elements (lines, points) to existing plots.

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link

Note: Part I of UsingR is complemented and extended by Part II, which is offered during the second part of the semester and which can be taken independently from Part I.
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeThe course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
401-6217-00LUsing R for Data Analysis and Graphics (Part II) Information W1.5 credits1GA. Drewek, M. Mächler
AbstractThe course provides the second part an introduction to the statistical software R for scientists. Topics are data generation and selection, graphical functions, important statistical functions, types of objects, models, programming and writing functions.
Note: This part builds on "Using R... (Part I)", but can be taken independently if the basics of R are already known.
ObjectiveThe students will be able to use the software R efficiently for data analysis.
ContentThe course provides the second part of an introduction to the statistical software R for scientists. R is free software that contains a huge collection of functions with focus on statistics and graphics. If one wants to use R one has to learn the programming language R - on very rudimentary level. The course aims to facilitate this by providing a basic introduction to R.

Part II of the course builds on part I and covers the following additional topics:
- Elements of the R language: control structures (if, else, loops), lists, overview of R objects, attributes of R objects;
- More on R functions;
- Applying functions to elements of vectors, matrices and lists;
- Object oriented programming with R: classes and methods;
- Tayloring R: options
- Extending basic R: packages

The course focuses on practical work at the computer. We will make use of the graphical user interface RStudio: Link
Lecture notesAn Introduction to R. Link
Prerequisites / NoticeBasic knowledge of R equivalent to "Using R .. (part 1)" ( = 401-6215-00L ) is a prerequisite for this course.

The course resources will be provided via the Moodle web learning platform
Please login (with your ETH (or other University) username+password) at
Link
Choose the course "Using R for Data Analysis and Graphics" and follow the instructions for registration.
Specialization in an Environmental System
Human-Environment Systems
NumberTitleTypeECTSHoursLecturers
701-0651-00LCoevolution between Society and Environment: Analysis and InfluenceW3 credits2VJ. Minsch
AbstractAnalysis of central mechanisms of the anthroposphere: ecological economics, theory of institutions and innovation, development economics.
ObjectiveIntroduction to the theoretical foundations of the analysis of central mechanisms of the anthroposphere – in a sustainable development perspective.

Knowledge of the different scientific and political discussions on sustainable development.

Knowledge of selected analytical tools (Ecological Economics, economic analysis of institutions, innovation theory, “Ordnungstheorie”, Theory of liberal economic policy).

Ability to identify central non sustainable mechanisms and policies, to formulate adequate research questions, to choose and to use adequate analytical tools, and to elaborate solutions.
ContentSustainable development-update: origins, conceptions, state of the discussion. What's left after 25 years of discussion?

Development as Freedom: Foundations of a human-rights-based Society and Economy (Amartya Sen, Daron Acemoglu / James A. Robinson, Ralf Dahrendorf, Friedrich. A. von Hayek, Karl. R. Popper. Walter Eucken).

Market Economy:
Its Critics, Reforms and new Developments.

An Inquiry into the Nature and Causes of ...Non-Sustainability:
Selected mechanisms and trends. The “neo-mercantilism-syndrom”

New Trends in the Growth Debate:
The Growth-spiral” (Hans Chr. Binswanger), Prosperity without growth? (T. Jackson), Intelligent Growth (R. Fücks)

The Internet of Things and Collaborative Commons - on the road to "The Zero Marginal Cost Society"?

Sufficiency: Perspectives of a resource-light society

Corporation 2020 - Transforming Business for Tomorrow's World (Remarks on Pavan Sukhdev's bestseller)

Finance Crash and Debt Crisis - new challenges for Democracy & Market Economy

Resourcecurse: Resources, democracy, and economic development

Globalization: Facts and elements of a fair globalization

It`s the software! Institutional Innovations for Sustainable Development. Let's continue writing The Federalist Papers!

On the way to the second "Great Transformation"

Perspectives for further, deeper analysis
Lecture notesskript and additional texts are distributed in the cource
LiteratureA first selection:
- Daron Acemoglu / James A. Robinson (2012): Why Nations Fail. The Origins of Power, Prosperity, and Poverty, New York
- Hans Christoph Binswanger (2006): Die Wachstumsspirale. Geld, Energie und Imagination in der Dynamik des Marksprozesses, Marburg
- Ralf Dahrendorf ( 2003): Auf der Suche nach einer neuen Ordnung, München
- Jared Diamond (2005): Collapse: How Societies Choose to Fail or Succeed, New York
- Ralf Fücks (2013): Intelligent wachsten, Die grüne Revolution, München
- Friedrich A. von Hayek (1991): Die Verfassung der Freiheit, 3. Auflage, Tübingen
- Friedrich A. von Hayek (1972): Theorie komplexer Phänomene, Tübingen
- Tim Jackson (2009): Prosperity without Growth. Economics for a Finite Planet, London
- Jürg Minsch / Peter H. Feindt / Hans. P. Meister / Uwe Schneidewind / Tobias Schulz (1998): Institutionelle Reformen für eine Politik der Nachhaltigkeit, Berlin / Heidelberg / New York
- J. Minsch / A. Eberle / B. Meier / U. Schneidewind (1996). Mut zum ökologischen Umbau. Innovationsstrategien für Unternehmen, Politik und Akteurnetze, Birkhäuser, Basel / Boston / Berlin
- Elinor Ostrom (1990): Governing the Commons, Cambridge University Press, Cambridge / New York / Melbourne
- oekom e.V., Hrsg. (2013): Baustelle Zukunft. die Grosse Trasformation von Wirtschaft und Gesellschaft, oekom Verlag, München
- Karl Polanyi (1944): The Great Transformation
- Karl. R. Popper (1980): Die offene Gesellschaft und ihre Feinde, Bde. I und II, 6. Auflage, Tübingen
Jeremy Rifkin (2014): The Zero Mrginal Cost Society: The Internet of things, the Collaborative Commons, and the Eclipse of Capitalism, palgrave macmillan
- Uwe Schneidewind / Angelika Zahrnt (2013): Damit gutes Leben einfacher wird. Perspektiven einer Suffizienzpolitik, München
- Pavan Sukhdev (2012): Corporation 2020. Transforming Business for Tomorrow's World, Washington D.C.
- Tomas Sedlacek (2012): Die Ökonomie von Gut und Böse, München
- Amartya Sen (1999): Development as Freedom, New York 1999)
- Daniel Spreng /Thomas Flüeler /David Goldblatt /Jürg Minsch (2012): Tackling Long Term Global Energy Problems: The Contribution of Social Science, Dortrecht / Heidelberg / New York
- Joseph Stiglitz (2006): Making Globalization Work, New York 2006)
- Peter Ulrich (2005): Zivilisierte Marktwirtschaft, 2. Aufl., Freiburg
- WBGU Wissenschaftlicher Beirat der Bundesregierung Globale Umweltveränderungen (2011): Welt im Wandel. Gesellschaftsvertrag für eine Grosse Transformation, Zusammenfassung für Entscheidungsträger, WBGU, Berlin, Link

Further reading and citations are listed in the skript and mentioned in the course.
Prerequisites / NoticeWillingness to prepare intensively the topics and to participate actively in the course
Environmental Sciences Master Information
Major in Atmosphere and Climate
Hydrology and Water Cycle
NumberTitleTypeECTSHoursLecturers
701-1253-00LAnalysis of Climate and Weather Data Information W3 credits2GC. Frei
AbstractObservation networks and numerical climate and forcasting models deliver large primary datasets. The use of this data in practice and in research requires specific techniques of statistical data analysis. This lecture introduces a range of frequently used techniques, and enables students to apply them and to properly interpret their results.
ObjectiveObservation networks and numerical climate and forcasting models deliver large primary datasets. The use of this data in practice and in research requires specific techniques of statistical data analysis. This lecture introduces a range of frequently used techniques, and enables students to apply them and to properly interpret their results.
ContentIntroduction into the theoretical background and the practical application of methods of data analysis in meteorology and climatology.

Topics: exploratory methods, hypothesis testing, analysis of climate trends, measuring the skill of climate and forecasting models, analysis of extremes, principal component analysis and maximum covariance analysis.

The lecture also provides an introduction into R, a programming language and graphics tool frequently used for data analysis in meteorology and climatology. During hands-on computer exercises the student will become familiar with the practical application of the methods.
Lecture notesDocumentation and supporting material include:
- documented view graphs used during the lecture
- excercise sets and solutions
- R-packages with software and example datasets for exercise sessions

All material is made available via the lecture web-page.
LiteratureSuggested literature:
- Wilks D.S., 2005: Statistical Methods in the Atmospheric Science. (2nd edition). International Geophysical Series, Academic Press Inc. (London)
- Coles S., 2001: An introduction to statistical modeling of extreme values. Springer, London. 208 pp.
Prerequisites / NoticePrerequisites: Atmosphäre, Mathematik IV: Statistik, Anwendungsnahes Programmieren.
Major in Ecology and Evolution
C. Scientific Skills
Quantitative and Computational Expertise
NumberTitleTypeECTSHoursLecturers
701-1419-00LAnalysis of Ecological DataW3 credits2GS. Güsewell
AbstractThis class provides students with an overview of techniques for data analysis used in modern ecological research, as well as practical experience in running these analyses with R and interpreting the results. Topics include linear models, generalized linear models, mixed models, model selection and randomization methods.
ObjectiveStudents will be able to:
- describe the aims and principles of important techniques for the analysis of ecological data
- choose appropriate techniques for given problems and types of data
- evaluate assumptions and limitations
- implement the analyses in R
- represent the relevant results in graphs, tables and text
- interpret and evaluate the results in ecological terms
Content- Linear models for experimental and observational studies
- Model selection
- Introduction to likelihood inference and Bayesian statistics
- Analysis of counts and proportions (generalised linear models)
- Models for non-linear relationships
- Grouping and correlation structures (mixed models)
- Randomisation methods
Lecture notesLecture notes and additional reading will be available electronically a few days before the course
LiteratureSuggested books for additional reading (available electronically)
Zuur A, Ieno EN & Smith GM (2007) Analysing ecological data. Springer, Berlin.
Zuur A, Ieno EN, Walker NJ, Saveliev AA & Smith GM (2009) Mixed effects models and extensions in ecology with R. Springer, New York.
Faraway JJ (2006) Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. Taylor & Francis.
Prerequisites / NoticeTime schedule
The course takes place on Mondays 12:45-15:00 from 25 September until 27 November, with the final exam on Monday 4 December. The last two weeks of the semester are free.

Prerequisites
- Basic statistical training (e.g. Mathematik IV in D-USYS): Data distributions, descriptive statistics, hypothesis testing, linear regression, analysis of variance
- Basic experience in data handling and data analysis in R

Individual preparation
Students without the required knowledge are asked to contact the lecturer before the first lecture date for support with individual preparation.
Major in Environmental Systems Policy
Modeling and Statistical Analysis
NumberTitleTypeECTSHoursLecturers
860-0002-00LQuantitative Policy Analysis and ModelingO6 credits4GA. Patt, T. Schmidt, E. Trutnevyte, O. van Vliet
AbstractThe lectures will introduce students to the principles of quantitative policy analysis, namely the methods to predict and evaluate the social, economic, and environmental effects of alternative strategies to achieve public objectives. A series of graded assignments will give students an opportunity for students to apply those methods to a set of case studies
ObjectiveThe objectives of this course are to develop the following key skills necessary for policy analysts:
- Identifying the critical quantitative factors that are of importance to policy makers in a range of decision-making situations.
- Developing conceptual models of the types of processes and relationships governing these quantitative factors, including stock-flow dynamics, feedback loops, optimization, sources and effects of uncertainty, and agent coordination problems.
- Develop and program numerical models to simulate the processes and relationships, in order to identify policy problems and the effects of policy interventions.
- Communicate the findings from these simulations and associated analysis in a manner that makes transparent their theoretical foundation, the level and sources of uncertainty, and ultimately their applicability to the policy problem.
The course will proceed through a series of policy analysis and modeling exercises, involving real-world or hypothetical problems. The specific examples around which work will be done will concern the environment, energy, health, and natural hazards management.
Minors
Minor in Sustainable Energy Use
NumberTitleTypeECTSHoursLecturers
227-1631-00LEnergy System Analysis Information W4 credits3GG. Hug, S. Hellweg, F. Noembrini, A. Schlüter
AbstractThe course provides an introduction to the methods and tools for analysis of energy consumption, energy production and energy flows. Environmental aspects are included as well as economical considerations. Different sectors of the society are discussed, such as electric power, buildings, and transportation. Models for energy system analysis planning are introduced.
ObjectiveThe purpose of the course is to give the participants an overview of the methods and tools used for energy systems analysis and how to use these in simple practical examples.
ContentThe course gives an introduction to methods and tools for analysis of energy consumption, energy production and energy flows. Both larger systems, e.g. countries, and smaller systems, e.g. industries, homes, vehicles, are studied. The tools and methods are applied to various problems during the exercises. Different conventions of energy statistics used are introduced.

The course provides also an introduction to energy systems models for developing scenarios of future energy consumption and production. Bottom-up and Top-Down approaches are addressed and their features and applications discussed.

The course contains the following parts:
Part I: Energy flows and energy statistics
Part II: Environmental impacts
Part III: Electric power systems
Part IV: Energy in buildings
Part V: Energy in transportation
Part VI: Energy systems models
Lecture notesHandouts
LiteratureExcerpts from various books, e.g. K. Blok: Introduction to Energy Analysis, Techne Press, Amsterdam 2006, ISBN 90-8594-016-8
Course Units for Additional Admission Requirements
The courses below are only available for Master students with additional admission requirements.
NumberTitleTypeECTSHoursLecturers
701-0071-AALMathematics III: Systems Analysis
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-4 credits9RN. Gruber
AbstractThe objective of the systems analysis course is to deepen and illustrate the mathematical concepts on the basis of a series of very concrete examples. Topics covered include: linear box models with one or several variables, non-linear box models with one or several variables, time-discrete models, and continuous models in time and space.
ObjectiveLearning and applying of concepts (models) and quantitative methods to address concrete problems of environmental relevance. Understanding and applying the systems-analytic approach, i.e., Recognizing the core of the problem - simplification - quantitative approach - prediction.
ContentLink
Lecture notesOverhead slides will be made available through Ilias.
LiteratureImboden, D.S. and S. Pfenninger (2013) Introduction to Systems Analysis: Mathematically Modeling Natural Systems. Berlin Heidelberg: Springer Verlag.

Link
701-1901-AALSystems Analysis
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
E-4 credits9RN. Gruber
AbstractSystems analysis is about the application of mathematical concepts to solve real world problems in a quantitative manner. Areas covered include: Dynamic linear models with one and several variables, Non-linear models with one or several variables; discrete-time models; and continuous models in space and time.
ObjectiveThe goal of the course is to develop quantitative skills in order to understand and solve a range of typical environmental problems.
ContentThe subject of the exam is the content of my
undergraduate lecture series Systemanalyse I and II (see Link).
This course is closely aligned with the Imboden&Koch / Imboden&Pfenniger books, except that I essentially skip chapter 7.
Lecture notesNo script is available, but you can purchase the Imboden/Koch or Imboden/Pfenniger books (or download some of the chapters yourself) through the Springer Verlag:

English version:
Link

German version:
Link