312.100 (17W) Dynamische Systeme 1
Überblick
- Lehrende/r
- LV-Titel englisch Dynamical Systems 1
- LV-Art Vorlesung-Übung (prüfungsimmanente LV )
- Semesterstunde/n 2.0
- ECTS-Anrechnungspunkte 3.0
- Anmeldungen 14 (25 max.)
- Organisationseinheit
- Unterrichtssprache es wurde keine Unterrichtssprache angegeben
- LV-Beginn 04.10.2017
Zeit und Ort
LV-Beschreibung
Lehrmethodik inkl. Einsatz von eLearning-Tools
Lecture
Inhalt/e
A dynamical system describes the time-dependence of a given process. Analyzing the dynamical system helps to "predict the future" of the process. Many applications arise naturally from biology (population dynamics, epidemiology, neural networks etc.), physics (e.g. position (and velocity) of a particle/spacecraft/planet etc.), chemistry (e.g. reaction kinetics), economics (e.g. macroeconomic-, monetary- and business models) and weather forecast.
Basics: Invariant and minimal sets, limit sets, attractors
Discrete dynamical systems: Linear dynamical systems, linearization, invariance principle
Continuous dynamical systems: Lyapunov functions, planar equations (planar linear equations, Poincaré-Bendixson theory, closed orbits), stability
Literatur
See lecture notes.
Further literature:
H. Amann, Ordinary differential equations: An introduction to nonlinear analysis, de Gruyter, Berlin etc., 1990
R. Clarke Robinson, An introduction to dynamical systems - Continuous and discrete, AMS, Providence RI, 2012
Prüfungsinformationen
Prüfungsmethode/n
Written exam
Prüfungsinhalt/e
Contents of the lecture.
Beurteilungsschema
Note BenotungsschemaPosition im Curriculum
- Doktoratsprogramm Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(SKZ: ---, Version: 16W.1)
-
Fach: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Pflichtfach)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
- 312.100 Dynamische Systeme 1 (2.0h VU / 3.0 ECTS)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
-
Fach: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Pflichtfach)
- Masterstudium Technische Mathematik
(SKZ: 401, Version: 13W.1)
-
Fach: Analysis
(Pflichtfach)
-
Dynamische Systeme 1 (
2.0h VU / 3.0 ECTS)
- 312.100 Dynamische Systeme 1 (2.0h VU / 3.0 ECTS)
-
Dynamische Systeme 1 (
2.0h VU / 3.0 ECTS)
-
Fach: Analysis
(Pflichtfach)