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406-0252-AAL 7 Credits MSC D-USYS
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Mathematics II

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 15:46:58

Abstract

Continuation of the topics of Mathematics I. Main focus: multivariable calculus and partial 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

- Multivariable Differential Calculus: functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence. - Multivariable Integral Calculus: multiple integrals, line and surface integrals, work and flux, Green, Gauss and Stokes theorems, applications. - Partial Differential Equations: separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform.

Resources

Literature

- Thomas, G. B.: Thomas' Calculus, Parts 2 (Pearson Addison-Wesley). - Kreyszig, E.: Advanced Engineering Mathematics (John Wiley & Sons).

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 II
Self-study course. No presence required.
No time listed 210 h semesterly

Offered In