401-0251-00L Mathematics I
Semester | Autumn Semester 2019 |
Lecturers | A. Cannas da Silva |
Periodicity | yearly recurring course |
Language of instruction | German |
Courses
Number | Title | Hours | Lecturers | |||||||
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401-0251-00 V | Mathematik I: Analysis I und Lineare Algebra | 4 hrs |
| A. Cannas da Silva | ||||||
401-0251-00 U | Mathematik I: Analysis I und Lineare Algebra Groups are selected in myStudies. Die Übungen beginnen in der zweiten Semesterwoche. Mo 15-17 für Studiengang Umweltnaturwissenschaften. Mi 10-12 für Studiengang Erdwissenschaften. Mi 13-15 für Studiengänge Agrarwissenschaften bzw. Lebensmittelwissenschaften. | 2 hrs | A. Cannas da Silva |
Catalogue data
Abstract | This course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations. |
Objective | Mathematics 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. |
Content | 1. 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 / Notice | Prerequisites: 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. |
Performance assessment
Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a two-semester course together with 401-0252-00L Mathematics II (next semester) | |
For programme regulations (Examination block) | Bachelor's Degree Programme in Agricultural Sciences 2015; Version 01.03.2019 (Examination Block) Bachelor's Degree Programme in Environmental Sciences 2011; Version 12.01.2016 (Examination Block) Bachelor's Degree Programme in Environmental Sciences 2016; Version 29.09.2023 (Examination Block) Bachelor's Degree Programme in Food Science 2016; Version 25.05.2023 (Examination Block) Bachelor's Programme in Agricultural Science 2010; Version 13.10.2015 (Examination Block) Bachelor's Programme in Earth Sciences 2010; Version 24.02.2016 (Examination Block) Bachelor's Programme in Earth Sciences 2016 (Examination Block) Bachelor's Programme in Food Science 2010; Version 22.03.2016 (Examination Block) |
ECTS credits | 13 credits |
Performance assessment as a semester course (other programmes) | |
ECTS credits | 6 credits |
Examiners | A. Cannas da Silva |
Type | session examination |
Language of examination | German |
Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
Mode of examination | written 90 minutes |
Additional information on mode of examination | ACHTUNG: Die folgenden Angaben betreffen den JAHRESKURS. Im Rahmen der Leistungskontrolle zur Basisprüfung werden auch zwei freiwillige Multiple-Choice-Zwischenprüfungen angeboten. Die erste Zwischenprüfung findet in der ersten Woche des FS 2020 statt und umfasst den gesamten in der Mathematik-I-Vorlesung und den entsprechenden Übungsserien behandelten Stoff. Falls die Prozent-Note dieser ersten Zwischenprüfung besser ist als die Prozent-Note der Prüfung des Jahreskurses in der Sommerprüfungssession 2020 (bzw. Winterprüfungssession 2021), wird die Note dieser Zwischenprüfung zu 20% an die Endnote angerechnet. Die zweite Zwischenprüfung findet in der zweiten Hälfte vom April 2020 statt und umfasst die erste Hälfte des in der Mathematik-II-Vorlesung und den entsprechenden Übungsserien behandelten Stoffs. Falls die Prozent-Note dieser zweiten Zwischenprüfung besser ist als die Prozent-Note der Prüfung des Jahreskurses in der Sommerprüfungssession 2020 (bzw. Winterprüfungssession 2021), wird die Note dieser Zwischenprüfung zu 10% an die Endnote angerechnet. |
Written aids | 20 A4-Seiten (= 10 doppelseitige Blätter) Notizen. 1 Wörterbuch für fremdsprachige Studierende. Keine (Taschen)Rechner, keine Mobiltelefone. |
If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block. This information can be updated until the beginning of the semester; information on the examination timetable is binding. |
Learning materials
Literature | Hauptliteratur: "Analysis 1" von Thomas, Weir und Hass - nicht online |
Hauptliteratur: "Lineare Algebra - Eine Einführung" von Gramlich - online an der ETH | |
Only public learning materials are listed. |
Groups
401-0251-00 U | Mathematik I: Analysis I und Lineare Algebra | |||||||||||
Groups | G-01A |
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G-01B |
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G-06 |
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G-08 |
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Restrictions
Groups | Restrictions are listed under Groups |