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406-0251-AAL 6 Credits MSC D-USYS , D-BAUG
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Mathematics I

Lecturers & Examiners: Prof. Dr. Lorenz Halbeisen
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.
VVZ CR n/a

Last Updated: 2026-02-05 15:34:46

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. 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. 2. Single-Variable Calculus: review of differentiation, linearisation, Taylor polynomials, maxima and minima, antiderivative, fundamental theorem of calculus, integration methods, improper integrals. 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

- Bretscher, O.: Linear Algebra with Applications (Pearson Prentice Hall). - Thomas, G. B.: Thomas' Calculus, Part 1 - Early Transcendentals (Pearson Addison-Wesley).

Learning Materials (Links)

General Information

Language
English
Levels
MSC
Frequency
Semesterly recurring

Examination

Type
session examination
Mode
written 90 minutes
Aids
20 pages A4 (= 10 sheets of paper - front & back sides) summary. 1 English dictionary. No (pocket) calculators, no cellular phones.

Course Components

Type Title Time & Place Hours
revision course / private study Mathematics I
Self-study course. No presence required.
No time listed 180 h semesterly

Offered In