Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-80-17-M-6

Dynamical Systems (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-80-17-M-6 Dynamical Systems 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg. SuSe
Level [6] Master (General)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Notice

This module can be combined with the module [MAT-80-12A-M-4] to the module [MAT-80-18-M-4].

Without a proof of successful participation in the exercise classes, only 3 credit points will be awarded for the module.

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-80-17-K-6
Dynamical Systems
P 42 h 93 h
U-Schein
- PL1 4.5 irreg. SuSe
  • About [MAT-80-17-K-6]: Title: "Dynamical Systems"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-80-17-K-6]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 84227 ("Dynamical Systems")

Evaluation of grades

The grade of the module examination is also the module grade.


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

Upon successful completion of this module, the students have learnt methods used for qualitative treatment of dynamic systems and are able to apply them. They are able to comprehend and explain the propositions and proofs presented in the lecture. 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.

By completing the given exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. They have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.

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.

Registration

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

Requirements for attendance (informal)

Modules:

Courses

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-80-17-M-6]

Course of Study Section Choice/Obligation
[INF-88.79-SG] M.Sc. Computer Science Formal Fundamentals [WP] Compulsory Elective
[MAT-88.105-SG] M.Sc. Mathematics Applied Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International Applied Mathematics [WP] Compulsory Elective
[MAT-88.118-SG] M.Sc. Industrial Mathematics General Mathematics [WP] Compulsory Elective
[MAT-88.276-SG] M.Sc. Business Mathematics General Mathematics [WP] Compulsory Elective