312.100 (17W) Dynamical Systems 1

Wintersemester 2017/18

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First course session
04.10.2017 14:30 - 16:30 HS 11 On Campus
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Overview

Lecturer
Course title german Dynamische Systeme 1
Type Lecture - Practical class (continuous assessment course )
Hours per Week 2.0
ECTS credits 3.0
Registrations 14 (25 max.)
Organisational unit
Language of instruction no language of instruction was specified
Course begins on 04.10.2017

Time and place

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Course Information

Teaching methodology including the use of eLearning tools

Lecture

Course content

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

Literature

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

Examination information

Im Fall von online durchgeführten Prüfungen sind die Standards zu beachten, die die technischen Geräte der Studierenden erfüllen müssen, um an diesen Prüfungen teilnehmen zu können.

Examination methodology

Written exam

Examination topic(s)

Contents of the lecture.

Grading scheme

Grade / Grade grading scheme

Position in the curriculum

  • Thematic Doctoral Programme Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (SKZ: ---, Version: 16W.1)
    • Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (Compulsory subject)
      • Modeling-Analysis - Optimization of discrete, continuous and stochastic systems ( 0.0h XX / 0.0 ECTS)
        • 312.100 Dynamical Systems 1 (2.0h VU / 3.0 ECTS)
  • Master's degree programme Technical Mathematics (SKZ: 401, Version: 13W.1)
    • Subject: Analysis (Compulsory subject)
      • Dynamische Systeme 1 ( 2.0h VU / 3.0 ECTS)
        • 312.100 Dynamical Systems 1 (2.0h VU / 3.0 ECTS)

Equivalent courses for counting the examination attempts

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)
Wintersemester 2013/14
  • 312.100 VU Dynamische Systeme 1 (2.0h / 3.0ECTS)