## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-00-031-K-1

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 4.0 CP 78 h
2 V Lecture 28 h
1 U Exercise class (in small groups) 14 h
(2V+1U) 4.0 CP 42 h 78 h

## Basedata

SWS 2V+1U 4.0 CP = 120 h 1 Sem. in WiSe  Bachelor (General) [DE] German [MAT-Service] Mathematics for other Departments [NORM] Active

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## Contents

Basic concepts for the treatment of ordinary and partial differential equations:

A. Ordinary differential equations:

• first-order differential equations: existence and uniqueness, first-order autonomous differential equations, separation approach, variation of constants, explicitly solvable cases, initial value problems;
• linear differential equations: homogeneous linear systems, matrix-exponential function, variation of constants, differential equations of nth order.

B. Partial differential equations:

• classification and well-posedness of 2nd order partial differential equations;
• wave equation, Poisson's equation, Fourier transform;
• solution methods: separation approach, Fourier transformation.

C. Numerical solution of differential equations:

• single step method (implicit/explicit);
• Runge-Kutta method;
• step size control.

## Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

None

## References to Course [MAT-00-031-K-1]

Module Name Context
[BI-BSCBI-018-M-4] Höhere Mathematik für Bauingenieure III - Differentialgleichungen P: Obligatory 2V+1U, 4.0 LP
[MAT-00-03A-M-1] Higher Mathematics: Vector Analysis and Differential Equations (for Engineering Students) P: Obligatory 2V+1U, 4.0 LP
[MAT-00-03C-M-1] Higher Mathematics: Differential Equations and Numerics (for Engineering Students) P: Obligatory 2V+1U, 4.0 LP