312.100 (19W) Dynamical Systems 1
Überblick
- Lehrende/r
- LV-Titel englisch Dynamical Systems 1
- LV-Art Vorlesung
- Semesterstunde/n 2.0
- ECTS-Anrechnungspunkte 4.0
- Anmeldungen 5
- Organisationseinheit
- Unterrichtssprache Englisch
- mögliche Sprache/n der Leistungserbringung Englisch
- LV-Beginn 02.10.2019
- eLearning zum Moodle-Kurs
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, Hartman-Grobman theorem
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. We will agree on the details on the first week.
Prüfungsinhalt/e
Definitions, theorems, examples, proofs.
Beurteilungskriterien/-maßstäbe
50% of the points are sufficient in order to pass the exam.
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 Dynamical Systems 1 (2.0h VO / 4.0 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 (
2.0h VO / 4.0 ECTS)
- 312.100 Dynamical Systems 1 (2.0h VO / 4.0 ECTS)
-
4.1 Dynamical Systems 1 (
2.0h VO / 4.0 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)
- 312.100 Dynamical Systems 1 (2.0h VO / 4.0 ECTS)
-
Lehrveranstaltungen aus den Vertiefungsfächern (
0.0h XX / 12.0 ECTS)
-
Fach: Applied Mathematics
(Wahlfach)
- Masterstudium Technische Mathematik
(SKZ: 401, Version: 13W.1)
-
Fach: Analysis
(Pflichtfach)
-
Dynamische Systeme 1 (
2.0h VU / 3.0 ECTS)
- 312.100 Dynamical Systems 1 (2.0h VO / 4.0 ECTS)
-
Dynamische Systeme 1 (
2.0h VU / 3.0 ECTS)
-
Fach: Analysis
(Pflichtfach)
- 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)
- 312.100 Dynamical Systems 1 (2.0h VO / 4.0 ECTS)
-
Studienleistungen gem. § 3 Abs. 2a des Curriculums (
16.0h XX / 32.0 ECTS)
-
Fach: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Pflichtfach)
Gleichwertige Lehrveranstaltungen im Sinne der Prüfungsantrittszählung
-
Wintersemester 2023/24
- 312.106 VO Dynamical Systems 1 (2.0h / 3.0ECTS)
-
Wintersemester 2022/23
- 312.106 VO Dynamical Systems 1 (2.0h / 3.0ECTS)
-
Wintersemester 2021/22
- 312.100 VO Dynamical Systems 1 (2.0h / 4.0ECTS)
-
Wintersemester 2020/21
- 312.100 VO Dynamical Systems 1 (2.0h / 4.0ECTS)
-
Wintersemester 2018/19
- 312.100 VO Dynamical Systems 1 (2.0h / 4.0ECTS)