312.100 (17W) Dynamical Systems 1
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
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
Examination methodology
Written exam
Examination topic(s)
Contents of the lecture.
Grading scheme
Grade / Grade grading schemePosition 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)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
-
Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Compulsory subject)
- 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)
-
Dynamische Systeme 1 (
2.0h VU / 3.0 ECTS)
-
Subject: Analysis
(Compulsory subject)