312.101 (18W) Dynamical Systems 1, exercises
Überblick
- Lehrende/r
- LV-Titel englisch Dynamical Systems 1, exercises
- LV-Art Übung (prüfungsimmanente LV )
- Semesterstunde/n 1.0
- ECTS-Anrechnungspunkte 2.0
- Anmeldungen 2 (25 max.)
- Organisationseinheit
- Unterrichtssprache Englisch
- LV-Beginn 02.10.2018
Zeit und Ort
LV-Beschreibung
Lehrmethodik inkl. Einsatz von eLearning-Tools
Exercises
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
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)
- 312.101 Dynamical Systems 1, exercises (1.0h UE / 2.0 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 Mathematics
(SKZ: 401, Version: 18W.1)
-
Fach: Applied Analysis
(Wahlfach)
-
4.1 Dynamical Systems 1 (
1.0h UE / 2.0 ECTS)
- 312.101 Dynamical Systems 1, exercises (1.0h UE / 2.0 ECTS)
-
4.1 Dynamical Systems 1 (
1.0h UE / 2.0 ECTS)
-
Fach: Applied Analysis
(Wahlfach)
- Masterstudium Mathematics
(SKZ: 401, Version: 18W.1)
-
Fach: Applied Mathematics
(Wahlfach)
-
Lehrveranstaltungen aus den Vertiefungsfächern (
0.0h XX / 12.0 ECTS)
- 312.101 Dynamical Systems 1, exercises (1.0h UE / 2.0 ECTS)
-
Lehrveranstaltungen aus den Vertiefungsfächern (
0.0h XX / 12.0 ECTS)
-
Fach: Applied Mathematics
(Wahlfach)
- Masterstudium Technische Mathematik
(SKZ: 401, Version: 13W.1)
-
Fach: Angewandte Analysis
(Wahlfach)
-
Dynamische Systeme 2 (
3.0h VU / 6.0 ECTS)
- 312.101 Dynamical Systems 1, exercises (1.0h UE / 2.0 ECTS)
-
Dynamische Systeme 2 (
3.0h VU / 6.0 ECTS)
-
Fach: Angewandte Analysis
(Wahlfach)
- Doktoratsstudium Doktoratsstudium der Technischen Wissenschaften
(SKZ: 786, Version: 12W.4)
-
Fach: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Pflichtfach)
-
Studienleistungen gem. § 3 Abs. 2a des Curriculums (
16.0h XX / 32.0 ECTS)
- 312.101 Dynamical Systems 1, exercises (1.0h UE / 2.0 ECTS)
-
Studienleistungen gem. § 3 Abs. 2a des Curriculums (
16.0h XX / 32.0 ECTS)
-
Fach: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Pflichtfach)