Suchergebnis: Katalogdaten im Herbstsemester 2017
Rechnergestützte Wissenschaften Bachelor | ||||||
Vertiefungsgebiete | ||||||
Astrophysik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
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401-7851-00L | Theoretical Astrophysics (University of Zurich) Der Kurs muss direkt an der UZH belegt werden. UZH Modulkürzel: AST512 Beachten Sie die Einschreibungstermine an der UZH: Link | W | 10 KP | 4V + 2U | R. Teyssier | |
Kurzbeschreibung | This course covers the foundations of astrophysical fluid dynamics, the Boltzmann equation, equilibrium systems and their stability, the structure of stars, astrophysical turbulence, accretion disks and their stability, the foundations of radiative transfer, collisionless systems, the structure and stability of dark matter halos and galactic disks. | |||||
Lernziel | ||||||
Literatur | Course Materials: 1- The Physics of Astrophysics, Volume 1: Radiation by Frank H. Shu 2- The Physics of Astrophysics, Volume 2: Gas Dynamics by Frank H. Shu 3- Foundations of radiation hydrodynamics, Dimitri Mihalas and Barbara Weibel-Mihalas 4- Radiative Processes in Astrophysics, George B. Rybicki and Alan P. Lightman 5- Galactic Dynamics, James Binney and Scott Tremaine | |||||
Voraussetzungen / Besonderes | Prerequisites: Introduction to Astrophysics Mathematical Methods for the Physicist Quantum Mechanics (All preferred but not obligatory) Prior Knowledge: Mechanics Quantum Mechanics and atomic physics Thermodynamics Fluid Dynamics Electrodynamics | |||||
401-7855-00L | Computational Astrophysics (University of Zurich) Der Kurs muss direkt an der UZH belegt werden. UZH Modulkürzel: AST245 Beachten Sie die Einschreibungstermine an der UZH: Link | W | 6 KP | 2V | L. M. Mayer | |
Kurzbeschreibung | ||||||
Lernziel | Acquire knowledge of main methodologies for computer-based models of astrophysical systems,the physical equations behind them, and train such knowledge with simple examples of computer programmes | |||||
Inhalt | 1. Integration of ODE, Hamiltonians and Symplectic integration techniques, time adaptivity, time reversibility 2. Large-N gravity calculation, collisionless N-body systems and their simulation 3. Fast Fourier Transform and spectral methods in general 4. Eulerian Hydrodynamics: Upwinding, Riemann solvers, Limiters 5. Lagrangian Hydrodynamics: The SPH method 6. Resolution and instabilities in Hydrodynamics 7. Initial Conditions: Cosmological Simulations and Astrophysical Disks 8. Physical Approximations and Methods for Radiative Transfer in Astrophysics | |||||
Literatur | Galactic Dynamics (Binney & Tremaine, Princeton University Press), Computer Simulation using Particles (Hockney & Eastwood CRC press), Targeted journal reviews on computational methods for astrophysical fluids (SPH, AMR, moving mesh) | |||||
Voraussetzungen / Besonderes | Some knowledge of UNIX, scripting languages (see Link as an example), some prior experience programming, knowledge of C, C++ beneficial | |||||
Atmosphärenphysik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
701-0023-00L | Atmosphäre | W | 3 KP | 2V | E. Fischer, T. Peter | |
Kurzbeschreibung | Grundlagen der Atmosphäre, physikalischer Aufbau und chemische Zusammensetzung, Spurengase, Kreisläufe in der Atmosphäre, Zirkulation, Stabilität, Strahlung, Kondensation, Wolken, Oxidationspotential und Ozonschicht. | |||||
Lernziel | Verständnis grundlegender physikalischer und chemischer Prozesse in der Atmosphäre. Kenntnis über die Mechanismen und Zusammenhänge von: Wetter - Klima, Atmosphäre - Ozeane - Kontinente, Troposphäre - Stratosphäre. Verständnis von umweltrelevanten Strukturen und Vorgängen in sehr unterschiedlichem Massstab. Grundlagen für eine modellmässige Darstellung komplexer Zusammenhänge in der Atmosphäre. | |||||
Inhalt | Grundlagen der Atmosphäre, physikalischer Aufbau und chemische Zusammensetzung, Spurengase, Kreisläufe in der Atmosphäre, Zirkulation, Stabilität, Strahlung, Kondensation, Wolken, Oxidationspotential und Ozonschicht. | |||||
Skript | Schriftliche Unterlagen werden abgegeben. | |||||
Literatur | - John H. Seinfeld and Spyros N. Pandis, Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, Wiley, New York, 1998. - Gösta H. Liljequist, Allgemeine Meteorologie, Vieweg, Braunschweig, 1974. | |||||
Chemie | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
529-0004-00L | Computer Simulation in Chemistry, Biology and Physics | W | 7 KP | 4G | P. H. Hünenberger | |
Kurzbeschreibung | Molecular models, Force fields, Boundary conditions, Electrostatic interactions, Molecular dynamics, Analysis of trajectories, Quantum-mechanical simulation, Structure refinement, Application to real systems. Exercises: Analysis of papers on computer simulation, Molecular simulation in practice, Validation of molecular dynamics simulation. | |||||
Lernziel | Introduction to computer simulation of (bio)molecular systems, development of skills to carry out and interpret computer simulations of biomolecular systems. | |||||
Inhalt | Molecular models, Force fields, Spatial boundary conditions, Calculation of Coulomb forces, Molecular dynamics, Analysis of trajectories, Quantum-mechanical simulation, Structure refinement, Application to real systems. Exercises: Analysis of papers on computer simulation, Molecular simulation in practice, Validation of molecular dynamics simulation. | |||||
Skript | Available (copies of powerpoint slides distributed before each lecture) | |||||
Literatur | See: Link | |||||
Voraussetzungen / Besonderes | Since the exercises on the computer do convey and test essentially different skills as those being conveyed during the lectures and tested at the oral exam, the results of the exercises are taken into account when evaluating the results of the exam. For more information about the lecture: Link | |||||
Fluiddynamik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
151-0103-00L | Fluiddynamik II | W | 3 KP | 2V + 1U | P. Jenny | |
Kurzbeschreibung | Ebene Potentialströmungen: Stromfunktion und Potential, Singularitätenmethode, instationäre Strömung, aerodynamische Begriffe. Drehungsbehaftete Strömungen: Wirbelstärke und Zirkulation, Wirbeltransportgleichung, Wirbelsätze von Helmholtz und Kelvin. Kompressible Strömungen: Stromfadentheorie, senkrechter und schiefer Verdichtungsstoss, Laval-Düse, Prandtl-Meyer-Expansion, Reibungseinfluss. | |||||
Lernziel | Erweiterung der Grundlagen der Fluiddynamik. Grundbegriffe, Phänomene und Gesetzmässigkeiten von drehungsfreien, drehungsbehafteten und eindimensionalen kompressiblen Strömungen vermitteln. | |||||
Inhalt | Ebene Potentialströmungen: Stromfunktion und Potential, komplexe Darstellung, Singularitätenmethode, instationäre Strömung, aerodynamische Begriffe. Drehungsbehaftete Strömungen: Wirbelstärke und Zirkulation, Wirbeldynamik und Wirbeltransportgleichung, Wirbelsätze von Helmholtz und Kelvin. Kompressible Strömungen: Stromfadentheorie, senkrechter und schiefer Verdichtungsstoss, Laval-Düse, Prandtl-Meyer-Expansion, Reibungseinfluss. | |||||
Skript | ja (Siehe auch untenstehende Information betreffend der Literatur.) | |||||
Literatur | P.K. Kundu, I.M. Cohen, D.R. Dowling: Fluid Mechanics, Academic Press, 5th ed., 2011 (includes a free copy of the DVD "Multimedia Fluid Mechanics") P.K. Kundu, I.M. Cohen, D.R. Dowling: Fluid Mechanics, Academic Press, 6th ed., 2015 (does NOT include a free copy of the DVD "Multimedia Fluid Mechanics") | |||||
Voraussetzungen / Besonderes | Analysis I/II, Fluiddynamik I, Grundbegriffe der Thermodynamik (Thermodynamik I). Für die Formulierung der Grundlagen der Fluiddynamik werden unabdingbar Begriffe und Ergebnisse aus der Mathematik benötigt. Erfahrungsgemäss haben einige Studierende damit Schwierigkeiten. Es wird daher dringend empfohlen, insbesondere den Stoff über - elementare Funktionen (wie sin, cos, tan, exp, deren Umkehrfunktionen, Ableitungen und Integrale) sowie über - Vektoranalysis (Gradient, Divergenz, Rotation, Linienintegral ("Arbeit"), Integralsätze von Gauss und von Stokes, Potentialfelder als Lösungen der Laplace-Gleichung) zu wiederholen. Ferner wird der Umgang mit - komplexen Zahlen und Funktionen (siehe Anhang des Skripts Analysis I/II Teil C und Zusammenfassung im Anhang C des Skripts Fluiddynamik) benötigt. Literatur z.B.: U. Stammbach: Analysis I/II, Skript Teile A, B und C. | |||||
Systems and Control | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
227-0103-00L | Regelsysteme | W | 6 KP | 2V + 2U | F. Dörfler | |
Kurzbeschreibung | Study of concepts and methods for the mathematical description and analysis of dynamical systems. The concept of feedback. Design of control systems for single input - single output and multivariable systems. | |||||
Lernziel | Study of concepts and methods for the mathematical description and analysis of dynamical systems. The concept of feedback. Design of control systems for single input - single output and multivariable systems. | |||||
Inhalt | Process automation, concept of control. Modelling of dynamical systems - examples, state space description, linearisation, analytical/numerical solution. Laplace transform, system response for first and second order systems - effect of additional poles and zeros. Closed-loop control - idea of feedback. PID control, Ziegler - Nichols tuning. Stability, Routh-Hurwitz criterion, root locus, frequency response, Bode diagram, Bode gain/phase relationship, controller design via "loop shaping", Nyquist criterion. Feedforward compensation, cascade control. Multivariable systems (transfer matrix, state space representation), multi-loop control, problem of coupling, Relative Gain Array, decoupling, sensitivity to model uncertainty. State space representation (modal description, controllability, control canonical form, observer canonical form), state feedback, pole placement - choice of poles. Observer, observability, duality, separation principle. LQ Regulator, optimal state estimation. | |||||
Literatur | K. J. Aström & R. Murray. Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press, 2010. R. C. Dorf and R. H. Bishop. Modern Control Systems. Prentice Hall, New Jersey, 2007. G. F. Franklin, J. D. Powell, and A. Emami-Naeini. Feedback Control of Dynamic Systems. Addison-Wesley, 2010. J. Lunze. Regelungstechnik 1. Springer, Berlin, 2014. J. Lunze. Regelungstechnik 2. Springer, Berlin, 2014. | |||||
Voraussetzungen / Besonderes | Prerequisites: Signal and Systems Theory II. MATLAB is used for system analysis and simulation. | |||||
227-0045-00L | Signal- und Systemtheorie I | W | 4 KP | 2V + 2U | H. Bölcskei | |
Kurzbeschreibung | Signaltheorie und Systemtheorie (zeitkontinuierlich und zeitdiskret): Signalanalyse im Zeit- und Frequenzbereich, Signalräume, Hilberträume, verallgemeinerte Funktionen, lineare zeitinvariante Systeme, Abtasttheoreme, zeitdiskrete Signale und Systeme, digitale Filterstrukturen, diskrete Fourier-Transformation (DFT), endlich-dimensionale Signale und Systeme, schnelle Fouriertransformation (FFT). | |||||
Lernziel | Einführung in die mathematische Signaltheorie und Systemtheorie. | |||||
Inhalt | Signaltheorie und Systemtheorie (zeitkontinuierlich und zeitdiskret): Signalanalyse im Zeit- und Frequenzbereich, Signalräume, Hilberträume, verallgemeinerte Funktionen, lineare zeitinvariante Systeme, Abtasttheoreme, zeitdiskrete Signale und Systeme, digitale Filterstrukturen, diskrete Fourier-Transformation (DFT), endlich-dimensionale Signale und Systeme, schnelle Fouriertransformation (FFT). | |||||
Skript | Vorlesungsskriptum, Übungsskriptum mit Lösungen. | |||||
Robotik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
151-0601-00L | Theory of Robotics and Mechatronics | W | 4 KP | 3G | P. Korba, S. Stoeter | |
Kurzbeschreibung | This course provides an introduction and covers the fundamentals of the field, including rigid motions, homogeneous transformations, forward and inverse kinematics of multiple degree of freedom manipulators, velocity kinematics, motion planning, trajectory generation, sensing, vision, and control. It’s a requirement for the Robotics Vertiefung and for the Masters in Mechatronics and Microsystems. | |||||
Lernziel | Robotics is often viewed from three perspectives: perception (sensing), manipulation (affecting changes in the world), and cognition (intelligence). Robotic systems integrate aspects of all three of these areas. This course provides an introduction to the theory of robotics, and covers the fundamentals of the field, including rigid motions, homogeneous transformations, forward and inverse kinematics of multiple degree of freedom manipulators, velocity kinematics, motion planning, trajectory generation, sensing, vision, and control. This course is a requirement for the Robotics Vertiefung and for the Masters in Mechatronics and Microsystems. | |||||
Inhalt | An introduction to the theory of robotics, and covers the fundamentals of the field, including rigid motions, homogeneous transformations, forward and inverse kinematics of multiple degree of freedom manipulators, velocity kinematics, motion planning, trajectory generation, sensing, vision, and control. | |||||
Skript | available. | |||||
Voraussetzungen / Besonderes | The course will be taught in English. | |||||
252-0535-00L | Machine Learning | W | 8 KP | 3V + 2U + 2A | J. M. Buhmann | |
Kurzbeschreibung | Machine learning algorithms provide analytical methods to search data sets for characteristic patterns. Typical tasks include the classification of data, function fitting and clustering, with applications in image and speech analysis, bioinformatics and exploratory data analysis. This course is accompanied by practical machine learning projects. | |||||
Lernziel | Students will be familiarized with the most important concepts and algorithms for supervised and unsupervised learning; reinforce the statistics knowledge which is indispensible to solve modeling problems under uncertainty. Key concepts are the generalization ability of algorithms and systematic approaches to modeling and regularization. A machine learning project will provide an opportunity to test the machine learning algorithms on real world data. | |||||
Inhalt | The theory of fundamental machine learning concepts is presented in the lecture, and illustrated with relevant applications. Students can deepen their understanding by solving both pen-and-paper and programming exercises, where they implement and apply famous algorithms to real-world data. Topics covered in the lecture include: - Bayesian theory of optimal decisions - Maximum likelihood and Bayesian parameter inference - Classification with discriminant functions: Perceptrons, Fisher's LDA and support vector machines (SVM) - Ensemble methods: Bagging and Boosting - Regression: least squares, ridge and LASSO penalization, non-linear regression and the bias-variance trade-off - Non parametric density estimation: Parzen windows, nearest nieghbour - Dimension reduction: principal component analysis (PCA) and beyond | |||||
Skript | No lecture notes, but slides will be made available on the course webpage. | |||||
Literatur | C. Bishop. Pattern Recognition and Machine Learning. Springer 2007. R. Duda, P. Hart, and D. Stork. Pattern Classification. John Wiley & Sons, second edition, 2001. T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer, 2001. L. Wasserman. All of Statistics: A Concise Course in Statistical Inference. Springer, 2004. | |||||
Voraussetzungen / Besonderes | The course requires solid basic knowledge in analysis, statistics and numerical methods for CSE as well as practical programming experience for solving assignments. Students should at least have followed one previous course offered by the Machine Learning Institute (e.g., CIL or LIS) or an equivalent course offered by another institution. | |||||
263-3210-00L | Deep Learning Maximale Teilnehmerzahl: 300 | W | 4 KP | 2V + 1U | T. Hofmann | |
Kurzbeschreibung | Deep learning is an area within machine learning that deals with algorithms and models that automatically induce multi-level data representations. | |||||
Lernziel | In recent years, deep learning and deep networks have significantly improved the state-of-the-art in many application domains such as computer vision, speech recognition, and natural language processing. This class will cover the mathematical foundations of deep learning and provide insights into model design, training, and validation. The main objective is a profound understanding of why these methods work and how. There will also be a rich set of hands-on tasks and practical projects to familiarize students with this emerging technology. | |||||
Voraussetzungen / Besonderes | This is an advanced level course that requires some basic background in machine learning. More importantly, students are expected to have a very solid mathematical foundation, including linear algebra, multivariate calculus, and probability. The course will make heavy use of mathematics and is not (!) meant to be an extended tutorial of how to train deep networks with tools like Torch or Tensorflow, although that may be a side benefit. The participation in the course is subject to the following conditions: 1) The number of participants is limited to 300 students (MSc and PhDs). 2) Students must have taken the exam in Machine Learning (252-0535-00) or have acquired equivalent knowledge, see exhaustive list below: Machine Learning Link Computational Intelligence Lab Link Learning and Intelligent Systems Link Statistical Learning Theory Link Computational Statistics Link Probabilistic Artificial Intelligence Link Data Mining: Learning from Large Data Sets Link | |||||
263-5902-00L | Computer Vision | W | 6 KP | 3V + 1U + 1A | L. Van Gool, V. Ferrari, A. Geiger | |
Kurzbeschreibung | The goal of this course is to provide students with a good understanding of computer vision and image analysis techniques. The main concepts and techniques will be studied in depth and practical algorithms and approaches will be discussed and explored through the exercises. | |||||
Lernziel | The objectives of this course are: 1. To introduce the fundamental problems of computer vision. 2. To introduce the main concepts and techniques used to solve those. 3. To enable participants to implement solutions for reasonably complex problems. 4. To enable participants to make sense of the computer vision literature. | |||||
Inhalt | Camera models and calibration, invariant features, Multiple-view geometry, Model fitting, Stereo Matching, Segmentation, 2D Shape matching, Shape from Silhouettes, Optical flow, Structure from motion, Tracking, Object recognition, Object category recognition | |||||
Voraussetzungen / Besonderes | It is recommended that students have taken the Visual Computing lecture or a similar course introducing basic image processing concepts before taking this course. | |||||
151-0563-01L | Dynamic Programming and Optimal Control | W | 4 KP | 2V + 1U | R. D'Andrea | |
Kurzbeschreibung | Introduction to Dynamic Programming and Optimal Control. | |||||
Lernziel | Covers the fundamental concepts of Dynamic Programming & Optimal Control. | |||||
Inhalt | Dynamic Programming Algorithm; Deterministic Systems and Shortest Path Problems; Infinite Horizon Problems, Bellman Equation; Deterministic Continuous-Time Optimal Control. | |||||
Literatur | Dynamic Programming and Optimal Control by Dimitri P. Bertsekas, Vol. I, 3rd edition, 2005, 558 pages, hardcover. | |||||
Voraussetzungen / Besonderes | Requirements: Knowledge of advanced calculus, introductory probability theory, and matrix-vector algebra. | |||||
151-0851-00L | Robot Dynamics | W | 4 KP | 2V + 1U | M. Hutter, R. Siegwart | |
Kurzbeschreibung | We will provide an overview on how to kinematically and dynamically model typical robotic systems such as robot arms, legged robots, rotary wing systems, or fixed wing. | |||||
Lernziel | The primary objective of this course is that the student deepens an applied understanding of how to model the most common robotic systems. The student receives a solid background in kinematics, dynamics, and rotations of multi-body systems. On the basis of state of the art applications, he/she will learn all necessary tools to work in the field of design or control of robotic systems. | |||||
Inhalt | The course consists of three parts: First, we will refresh and deepen the student's knowledge in kinematics, dynamics, and rotations of multi-body systems. In this context, the learning material will build upon the courses for mechanics and dynamics available at ETH, with the particular focus on their application to robotic systems. The goal is to foster the conceptual understanding of similarities and differences among the various types of robots. In the second part, we will apply the learned material to classical robotic arms as well as legged systems and discuss kinematic constraints and interaction forces. In the third part, focus is put on modeling fixed wing aircraft, along with related design and control concepts. In this context, we also touch aerodynamics and flight mechanics to an extent typically required in robotics. The last part finally covers different helicopter types, with a focus on quadrotors and the coaxial configuration which we see today in many UAV applications. Case studies on all main topics provide the link to real applications and to the state of the art in robotics. | |||||
Voraussetzungen / Besonderes | The contents of the following ETH Bachelor lectures or equivalent are assumed to be known: Mechanics and Dynamics, Control, Basics in Fluid Dynamics. | |||||
Physik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
402-0809-00L | Introduction to Computational Physics | W | 8 KP | 2V + 2U | H. J. Herrmann | |
Kurzbeschreibung | Diese Vorlesung bietet eine Einführung in Computersimulationsmethoden für physikalische Probleme und deren Implementierung auf PCs und Supercomputern: klassische Bewegungsgleichungen, partielle Differentialgleichungen (Wellengleichung, Diffussionsgleichung, Maxwell-Gleichungen), Monte Carlo Simulation, Perkolation, Phasenübergänge | |||||
Lernziel | ||||||
Inhalt | Einführung in die rechnergestützte Simulation physikalischer Probleme. Anhand einfacher Modelle aus der klassischen Mechanik, Elektrodynamik und statistischen Mechanik sowie interdisziplinären Anwendungen werden die wichtigsten objektorientierten Programmiermethoden für numerische Simulationen (überwiegend in C++) erläutert. Daneben wird eine Einführung in die Programmierung von Vektorsupercomputern und parallelen Rechnern, sowie ein Überblick über vorhandene Softwarebibliotheken für numerische Simulationen geboten. | |||||
Voraussetzungen / Besonderes | Vorlesung und Uebung in Englisch, Pruefung wahlweise auf Deutsch oder Englisch | |||||
Computational Finance | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3913-01L | Mathematical Foundations for Finance | W | 4 KP | 3V + 2U | M. Schweizer, E. W. Farkas | |
Kurzbeschreibung | First introduction to main modelling ideas and mathematical tools from mathematical finance | |||||
Lernziel | This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It mainly aims at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest.. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs. | |||||
Inhalt | Topics to be covered include - financial market models in finite discrete time - absence of arbitrage and martingale measures - valuation and hedging in complete markets - basics about Brownian motion - stochastic integration - stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem - Black-Scholes formula | |||||
Skript | Lecture notes will be sold at the beginning of the course. | |||||
Literatur | Lecture notes will be sold at the beginning of the course. Additional (background) references are given there. | |||||
Voraussetzungen / Besonderes | Prerequisites: Results and facts from probability theory as in the book "Probability Essentials" by J. Jacod and P. Protter will be used freely. Especially participants without a direct mathematics background are strongly advised to familiarise themselves with those tools before (or very quickly during) the course. (A possible alternative to the above English textbook are the (German) lecture notes for the standard course "Wahrscheinlichkeitstheorie".) For those who are not sure about their background, we suggest to look at the exercises in Chapters 8, 9, 22-25, 28 of the Jacod/Protter book. If these pose problems, you will have a hard time during the course. So be prepared. | |||||
401-4657-00L | Numerical Analysis of Stochastic Ordinary Differential Equations Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" | W | 6 KP | 3V + 1U | A. Jentzen | |
Kurzbeschreibung | Course 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. | |||||
Lernziel | The 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. | |||||
Inhalt | Generation 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 | |||||
Skript | Lecture Notes are available in the lecture homepage (please follow the link in the Learning materials section). | |||||
Literatur | P. 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. | |||||
Voraussetzungen / Besonderes | Prerequisites: 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. | |||||
Electromagnetics | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
227-2037-00L | Physical Modelling and Simulation | W | 6 KP | 4G | J. Smajic | |
Kurzbeschreibung | This module consists of (a) an introduction to fundamental equations of electromagnetics, mechanics and heat transfer, (b) a detailed overview of numerical methods for field simulations, and (c) practical examples solved in form of small projects. | |||||
Lernziel | Basic knowledge of the fundamental equations and effects of electromagnetics, mechanics, and heat transfer. Knowledge of the main concepts of numerical methods for physical modelling and simulation. Ability (a) to develop own simple field simulation programs, (b) to select an appropriate field solver for a given problem, (c) to perform field simulations, (d) to evaluate the obtained results, and (e) to interactively improve the models until sufficiently accurate results are obtained. | |||||
Inhalt | The module begins with an introduction to the fundamental equations and effects of electromagnetics, mechanics, and heat transfer. After the introduction follows a detailed overview of the available numerical methods for solving electromagnetic, thermal and mechanical boundary value problems. This part of the course contains a general introduction into numerical methods, differential and integral forms, linear equation systems, Finite Difference Method (FDM), Boundary Element Method (BEM), Method of Moments (MoM), Multiple Multipole Program (MMP) and Finite Element Method (FEM). The theoretical part of the course finishes with a presentation of multiphysics simulations through several practical examples of HF-engineering such as coupled electromagnetic-mechanical and electromagnetic-thermal analysis of MEMS. In the second part of the course the students will work in small groups on practical simulation problems. For solving practical problems the students can develop and use own simulation programs or chose an appropriate commercial field solver for their specific problem. This practical simulation work of the students is supervised by the lecturers. | |||||
Geophysik Empfohlene Kombinationen: Fach 1 + Fach 2 Fach 1 + Fach 3 Fach 2 + Fach 3 Fach 3 + Fach 4 Fach 5 + Fach 6 Fach 5 + Fach 4 | ||||||
Geophysik: Fach 1 | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
651-4007-00L | Continuum Mechanics | W | 3 KP | 2V | T. Gerya | |
Kurzbeschreibung | In this course, students learn crucial partial differential equations (conservation laws) that are applicable to any continuum including the Earth's mantle, core, atmosphere and ocean. The course will provide step-by-step introduction into the mathematical structure, physical meaning and analytical solutions of the equations. The course has a particular focus on solid Earth applications. | |||||
Lernziel | The goal of this course is to learn and understand few principal partial differential equations (conservation laws) that are applicable for analysing and modelling of any continuum including the Earth's mantle, core, atmosphere and ocean. By the end of the course, students should be able to write, explain and analyse the equations and apply them for simple analytical cases. Numerical solving of these equations will be discussed in the Numerical Modelling I and II course running in parallel. | |||||
Inhalt | A provisional week-by-week schedule (subject to change) is as follows: Week 1: The continuity equation Theory: Definition of a geological media as a continuum. Field variables used for the representation of a continuum.Methods for definition of the field variables. Eulerian and Lagrangian points of view. Continuity equation in Eulerian and Lagrangian forms and their derivation. Advective transport term. Continuity equation for an incompressible fluid. Exercise: Computing the divergence of velocity field. Week 2: Density and gravity Theory: Density of rocks and minerals. Thermal expansion and compressibility. Dependence of density on pressure and temperature. Equations of state. Poisson equation for gravitational potential and its derivation. Exercise: Computing density, thermal expansion and compressibility from an equation of state. Week 3: Stress and strain Theory: Deformation and stresses. Definition of stress, strain and strain-rate tensors. Deviatoric stresses. Mean stress as a dynamic (nonlithostatic) pressure. Stress and strain rate invariants. Exercise: Analysing strain rate tensor for solid body rotation. Week 4: The momentum equation Theory: Momentum equation. Viscosity and Newtonian law of viscous friction. Navier-–Stokes equation for the motion of a viscous fluid. Stokes equation of slow laminar flow of highly viscous incompressible fluid and its application to geodynamics. Simplification of the Stokes equation in case of constant viscosity and its relation to the Poisson equation. Exercises: Computing velocity for magma flow in a channel. Week 5: Viscous rheology of rocks Theory: Solid-state creep of minerals and rocks as themajor mechanism of deformation of the Earth’s interior. Dislocation and diffusion creep mechanisms. Rheological equations for minerals and rocks. Effective viscosity and its dependence on temperature, pressure and strain rate. Formulation of the effective viscosity from empirical flow laws. Exercise: Deriving viscous rheological equations for computing effective viscosities from empirical flow laws. Week 6: The heat conservation equation Theory: Fourier’s law of heat conduction. Heat conservation equation and its derivation. Radioactive, viscous and adiabatic heating and their relative importance. Heat conservation equation for the case of a constant thermal conductivity and its relation to the Poisson equation. Exercise: steady temperature profile in case of channel flow. Week 7: Elasticity and plasticity Theory: Elastic rheology. Maxwell viscoelastic rheology. Plastic rheology. Plastic yielding criterion. Plastic flow potential. Plastic flow rule. GRADING will be based on honeworks (30%) and oral exams (70%). Exam questions: Link | |||||
Skript | Script is available by request to Link Exam questions: Link | |||||
Literatur | Taras Gerya Introduction to Numerical Geodynamic Modelling Cambridge University Press, 2010 | |||||
Geophysik: Fach 2 | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
651-4241-00L | Numerical Modelling I and II: Theory and Applications | W | 6 KP | 4G | T. Gerya | |
Kurzbeschreibung | In this 13-week sequence, students learn how to write programs from scratch to solve partial differential equations that are useful for Earth science applications. Programming will be done in MATLAB and will use the finite-difference method and marker-in-cell technique. The course will emphasise a hands-on learning approach rather than extensive theory. | |||||
Lernziel | The goal of this course is for students to learn how to program numerical applications from scratch. By the end of the course, students should be able to write state-of-the-art MATLAB codes that solve systems of partial-differential equations relevant to Earth and Planetary Science applications using finite-difference method and marker-in-cell technique. Applications include Poisson equation, buoyancy driven variable viscosity flow, heat diffusion and advection, and state-of-the-art thermomechanical code programming. The emphasis will be on commonality, i.e., using a similar approach to solve different applications, and modularity, i.e., re-use of code in different programs. The course will emphasise a hands-on learning approach rather than extensive theory, and will begin with an introduction to programming in MATLAB. | |||||
Inhalt | A provisional week-by-week schedule (subject to change) is as follows: Week 1: Introduction to the finite difference approximation to differential equations. Introduction to programming in Matlab. Solving of 1D Poisson equation. Week 2: Direct and iterative methods for obtaining numerical solutions. Solving of 2D Poisson equation with direct method. Solving of 2D Poisson equation with Gauss-Seidel and Jacobi iterative methods. Week 3: Solving momentum and continuity equations in case of constant viscosity with stream function/vorticity formulation. Weeks 4: Staggered grid for formulating momentum and continuity equations. Indexing of unknowns. Solving momentum and continuity equations in case of constant viscosity using pressure-velocity formulation with staggered grid. Weeks 5: Conservative finite differences for the momentum equation. "Free slip" and "no slip" boundary conditions. Solving momentum and continuity equations in case of variable viscosity using pressure-velocity formulation with staggered grid. Week 6: Advection in 1-D. Eulerian methods. Marker-in-cell method. Comparison of different advection methods and their accuracy. Week 7: Advection in 2-D with Marker-in-cell method. Combining flow calculation and advection for buoyancy driven flow. Week 8: "Free surface" boundary condition and "sticky air" approach. Free surface stabilization. Runge-Kutta schemes. Week 9: Solving 2D heat conservation equation in case of constant thermal conductivity with explicit and implicit approaches. Week 10: Solving 2D heat conservation equation in case of variable thermal conductivity with implicit approach. Temperature advection with markers. Creating thermomechanical code by combining mechanical solution for 2D buoyancy driven flow with heat diffusion and advection based on marker-in-cell approach. Week 11: Subgrid diffusion of temperature. Implementing subgrid diffusion to the thermomechanical code. Week 12: Implementation of radioactive, adiabatic and shear heating to the thermomechanical code. Week 13: Implementation of temperature-, pressure- and strain rate-dependent viscosity, temperature- and pressure-dependent density and temperature-dependent thermal conductivity to the thermomechanical code. Final project description. GRADING will be based on weekly programming homeworks (50%) and a term project (50%) to develop an application of their choice to a more advanced level. | |||||
Literatur | Taras Gerya, Introduction to Numerical Geodynamic Modelling, Cambridge University Press 2010 | |||||
Geophysik: Fach 5 | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
651-4014-00L | Seismic Tomography | W | 3 KP | 2G | E. Kissling, T. Diehl, I. Molinari | |
Kurzbeschreibung | Seismic tomography is the science of interpreting seismic measurements (seismograms) to derive information about the structure of the Earth. The subject of this course is the formal relationship existing between a seismic measurement and the nature of the Earth, or of certain regions of the Earth, and the ways to use it, to gain information about the Earth. | |||||
Lernziel | ||||||
Literatur | Aki, K. and P. G. Richards, Quantitative Seismology, second edition, University Science Books, Sausalito, 2002. The most standard textbook in seismology, for grad students and advanced undergraduates. Dahlen, F. A. and J. Tromp, Theoretical Global Seismology, Princeton University Press, Princeton, 1998. A very good book, suited for advanced graduate students with a strong math background. Kennett B.L.N., The Seismic Wavefield. Volume I: Introduction and Theoretical Development (2001). Volume II: Interpretation of Seismograms on Regional and Global Scales (2002). Cambridge University Press. Lay, T. and T. C. Wallace, Modern Global Seismology, Academic Press, San Diego, 1995. A very basic seismology textbook. Chapters 2 through 4 provide a useful introduction to the contents of this course. Menke, W., Geophysical Data Analysis: Discrete Inverse Theory, revised edition, Academic Press, San Diego, 1989. A very complete textbook on inverse theory in geophysics. Press, W. H., S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes, Cambridge University Press. The art of scientific computing. Trefethen, L. N. and D. Bau III, Numerical Linear Algebra, Soc. for Ind. and Appl. Math., Philadelphia, 1997. A textbook on the numerical solution of large linear inverse problems, designed for advanced math undergraduates. |
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