## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-12-25-K-3

## Course Type

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

## Basedata

SWS 2V+1U 4.5 CP = 135 h 1 Sem. in SuSe [3] Bachelor (Core) [DE] German 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-GRU] Mathematics (B.Sc. year 1 and 2) [NORM] Active

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Examination number (Study achievement): 83120 ("Exercise Class Introduction to Ordinary Differential Equations")
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## Contents

• first-order differential equations: autonomous first-order differential equations, variation of constants, explicitly solvable cases, initial value problems,
• existence and uniqueness: functional-analytical foundations, Banach fixed-point theorem, Picard-Lindelöf theorem, the continuability of solutions, Peano's existence theorem,
• qualitative behaviour: Gronwall's lemma, continuous dependency on data, upper and lower functions,
• linear differential equations: homogeneous linear systems, matrix exponential function, variation of constants, nth-order differential equations,
• stability: dynamical systems, phase space, Hamiltonian systems, asymptotic behaviour, stability theory according to Lyapunov.

## Competencies / intended learning achievements

The students know the basic concepts, statements and methods of the theory of ordinary differential equations. By combining results from analysis and linear algebra, they are able to investigate advanced questions and solve minor application problems from science and technology using mathematical methods.

## Literature

• V.I. Arnold: Gewöhnliche Differentialgleichungen,
• L. Grüne, O. Junge: Gewöhnliche Differentialgleichungen,
• H. Heuser: Gewöhnliche Differentialgleichungen,
• J.W. Prüss, M. Wilke: Gewöhnliche Differentialgleichungen und dynamische Systeme,
• W. Walter: Gewöhnliche Differentialgleichungen,
• G. Teschl: Ordinary Differential Equations and Dynamic Systems.

## Materials

Further literature will be announced in the lecture(s); 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)

Knowledge of Linear Algebra from the course [MAT-10-12-K-2] or [MAT-10-12L-K-2].

None

## References to Course [MAT-12-25-K-3]

Module Name Context
[MAT-12-10P-M-3] Build-Up Module Mathematics (for Students of Physics) WP: Obligation to choose 2V+1U, 5.0 LP
[MAT-12-2-M-3] Measure Theory and Differential Equations P: Obligatory 2V+1U, 4.5 LP
[MAT-14-10L-M-3] Topic Module B: Mathematics as an Interdisciplinary Cross-Sectional Science WP: Obligation to choose 2V+1U, 4.5 LP
Course-Pool Name
[MAT-10-KPOOL-3] Pure Mathematics (B.Sc. Mathematics)
[PHY-M2-KPOOL-3] Höhere Analysis (für Studierende der Physik)