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Mathematics I
Mathematik I: Analysis I und Lineare Algebra
Last Updated: 2026-02-05 15:48:47
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.
Resources
Literature
- Thomas, G. B.: Thomas' Calculus, Part 1 (Pearson Addison-Wesley). - Bretscher, O.: Linear Algebra with Applications (Pearson Prentice Hall).
Learning Materials (Links)
General Information
- Language
- German
- Levels
- BSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 90 minutes
- Aids
- 20 A4-Seiten (= 10 doppelseitige Blätter) Notizen. 1 Wörterbuch für fremdsprachige Studierende. Keine (Taschen)Rechner, keine Mobiltelefone.
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Mathematik I: Analysis I und Lineare Algebra
Keine Präsenzvorlesung am 15. Dezember 2021. Stattdessen wird die Vorlesung in Zoom aufgezeichnet, und die Studierenden erhalten den Link.
Ebenso findet die Vorlesung am 20. Dezember 2021 nicht in Präsenz statt, sondern online per Zoom. Die Studierenden erhalten den Link per E-Mail.
ACHTUNG: Die Vorlesungen vom 22. und 23. Dezember finden, entgegen vorheriger Ankündigung, doch in Präsenz statt und werden von Jerome Wettstein gelesen.
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4 h weekly |
| exercise |
Mathematik I: Analysis I und Lineare Algebra
Groups are selected in myStudies.
Die Übungen beginnen in der zweiten Semesterwoche.
Mo 14-16 für Studiengänge Erd- und Klimawissenschaften bzw. Umweltnaturwissenschaften.
Di 14-16 für Studiengänge Agrarwissenschaften bzw. Lebensmittelwissenschaften.
Zusätzlich wird das Mathe-Lab (Präsenzstunden) angeboten: Mo 12-14 in HG D 1.2 und Di 16-18 in ML H 44.
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2 h weekly |
Offered In
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Environmental Sciences Bachelor (Students can choose between one Bachelor thesis of 10KP or two Bachelor theses of 5KP each. In principle, all professors and lecturers involved in the teaching of the Environmental Sciences degree programme are entitled to supervise a Bachelor's thesis (BA). BA in the area of social sciences and humanities can only be supervised by lecturers who teach in this area. The same applies to BA in the field of natural sciences and technology. If the thesis is supervised by a person who does not teach in the Environmental Sciences degree programme or who does not have ETH lecturer status, then the student has to fill in the "Form for supervisors of a Bachelor thesis who do not teach in the Environmental Sciences degree programme" Link)
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