## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-80-17-K-6

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
2 V Lecture 3.0 CP 28 h 62 h
1 U Exercise class (in small groups) 1.5 CP 14 h 31 h
(2V+1U) 4.5 CP 42 h 93 h

## Basedata

SWS 2V+1U 4.5 CP = 135 h 1 Sem. irreg. SuSe [6] Master (General) [EN] English Damm, Tobias, Prof. Dr. (PROF | DEPT: MAT) Surulescu, Christina, Prof. Dr. (PROF | DEPT: MAT) [MAT-TEMA] Industrial Mathematics [NORM] Active

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Examination number (Study achievement): 84027 ("Exercise Class Dynamical Systems")
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## Contents

• basics: existence and uniqueness,
• autonomous equations,
• stability theory,
• nonlinear systems, local theory, theorem of Hartman-Grobman, non hyperbolic equilibrium points and Lyapunov theory,
• periodic orbits, Poincaré Bendixon and applications, invariant sets,
• bifurcation theory,
• applications.

## Competencies / intended learning achievements

The students have studied methods for qualitative treatment of dynamic systems and are able to apply them. The focus is on the behavior of solutions of ordinary differential equations under the influence of varying parameters in a system. The techniques taught are very useful for the study of nonlinear partial differential equations and control theory as well as for the study of practical problems that are modeled by using differential equations.

## Literature

• J.K. Hale, H. Kocak: Dynamics and Bifurcations,
• H. Heuser: Gewöhnliche Differentialgleichungen,
• B. Marx, W. Vogt: Dynamische Systeme,
• J.W. Prüss, M. Wilke: Gewöhnliche Differentialgleichungen und dynamische Systeme.
• K. Burg, H. Haf, F. Wille, A. Meister: Höhere Mathematik für Ingenieure. Band III: Gewöhnliche Differentialgleichungen, Distributionen, Integraltransformationen.

## 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).

None

## References to Course [MAT-80-17-K-6]

Module Name Context
[MAT-80-17-M-6] Dynamical Systems P: Obligatory 2V+1U, 4.5 LP
[MAT-80-18-M-4] Introduction to Systems and Control Theory & Dynamical Systems P: Obligatory 2V+1U, 4.5 LP
Course-Pool Name
[MAT-70-2V-KPOOL-4] Elective Courses Analysis and Stochastics (2V, B.Sc.)
[MAT-80-2V-KPOOL-4] Elective Courses Modelling and Scientific Computing (2V, B.Sc.)