## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-80-11-K-4

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
4 V Lecture 6.0 CP 56 h 124 h
2 U Exercise class (in small groups) 3.0 CP 28 h 62 h
(4V+2U) 9.0 CP 84 h 186 h

## Basedata

SWS 4V+2U 9.0 CP = 270 h 1 Sem. in WiSe  Bachelor (Specialization) [EN] English Damm, Tobias, Prof. Dr. (PROF | DEPT: MAT) Klar, Axel, Prof. Dr. (PROF | DEPT: MAT) Pinnau, René, Prof. Dr. (PROF | DEPT: MAT) Simeon, Bernd, Prof. Dr. (PROF | DEPT: MAT) Surulescu, Christina, Prof. Dr. (PROF | DEPT: MAT) [MAT-TEMA] Industrial Mathematics [NORM] Active

## Notice

The course consists of the two parts [MAT-80-11A-K-4] and [MAT-80-11B-K-4].

## 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.
The certificate for the exercises ("Übungsschein") consists of the two (partial) certificates for the exercises in the courses [MAT-80-11A-K-4] and [MAT-80-11B-K-4].

## Contents

Numeric methods which deal with initial value problems will be discussed. In particular, the following contents are covered:
• One-step method (explicit/implicit): consistency, convergence, stability,
• Runge-Kutta methods,
• Control of step size,
• Methods for stiff problems: Gauß algorithm, collocation method.

This course gives an introduction to the classical theory of partial differential equations. In particular, the following contents are dealt with:

• Classification and well-posed problems,
• Quasilinear equations: Cauchy problem,
• Wave equation: existence, uniqueness, stability, maximum principle,
• Poisson equation: separation ansatz, fundamental solutions, Green's function, maximum principle, existence and uniqueness,
• Heat equation: separation of variables, Fourier transformation, semigroups, maximum principle, existence and uniqueness.

## Competencies / intended learning achievements

The students have studied and understand the fundamental concepts for numerical treatment of initial value problems, the mathematics techniques for analyzing the methods and the extension of the theory of ordinary differential equations (ODE) to partial differential equations (PDE).

## Literature

• P. Deuflhard, F. Bornemann: Numerische Mathematik II,
• J. Stoer, R. Bulirsch: Einführung in die Numerische Mathematik II,
• A. Quarteroni, R. Sacco, F. Saleri: Numerische Mathematik I, II,
• E. Hairer, G. Wanner: Solving Ordinary Differential Equations I, II,
• H. Heuser: Ordinary Differential Equations,
• W. Walter: Ordinary Differential Equations,
• G. Teschl: Ordinary Differential Equations and Dynamical Systems,
• L.C. Evans: Partial differential equations,
• F. John: Partial differential equations.

## Materials

Further literature will be announced in the lecture; Exercise material is provided.

## Registration

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

## Requirements for attendance (informal)

Desirable is knowledge from the course [MAT-12-27-K-3].

None

## References to Course [MAT-80-11-K-4]

Course-Pool Name
[MAT-70-4V-KPOOL-4] Elective Courses Analysis and Stochastics (4V, B.Sc.)
[MAT-70-KPOOL-4] Specialisation Analysis and Stochastics (B.Sc.)
[MAT-80-4V-KPOOL-4] Elective Courses Modelling and Scientific Computing (4V, B.Sc.)
[MAT-80-KPOOL-4] Specialisation Modelling and Scientific Computing (B.Sc.)