312.100 (17W) Dynamische Systeme 1

Wintersemester 2017/18

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Erster Termin der LV
04.10.2017 14:30 - 16:30 , HS 11
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Überblick

Lehrende/r
LV-Titel englisch
Dynamical Systems 1
LV-Art
Vorlesung-Übung (prüfungsimmanente LV )
Semesterstunde/n
2.0
ECTS-Anrechungspunkte
3.0
Anmeldungen
14 (25 max.)
Organisationseinheit
Unterrichtssprache
es wurde keine Unterrichtssprache angegeben
LV-Beginn
01.10.2017

LV-Beschreibung

Lehrmethodik

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/Grade Benotungsschema

Position 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)
  • 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)

Gleichwertige Lehrveranstaltungen im Sinne der Prüfungsantrittszählung

Wintersemester 2019/20
  • 312.100 VO Dynamical Systems 1 (2.0h / 4.0ECTS)
Wintersemester 2018/19
  • 312.100 VO Dynamical Systems 1 (2.0h / 4.0ECTS)
Wintersemester 2016/17
  • 312.100 VU Dynamische Systeme 1 (2.0h / 3.0ECTS)
Wintersemester 2015/16
  • 312.100 VU Dynamische Systeme 1 (2.0h / 3.0ECTS)
Wintersemester 2014/15
  • 312.100 VU Dynamische Systeme 1 (2.0h / 3.0ECTS)