312.106 (22W) Dynamical Systems 1
Überblick
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- Lehrende/r
- LV-Titel englisch Dynamical Systems 1
- LV-Art Vorlesung
- LV-Modell Präsenzlehrveranstaltung
- Semesterstunde/n 2.0
- ECTS-Anrechnungspunkte 3.0
- Anmeldungen 12
- Organisationseinheit
- Unterrichtssprache Englisch
- LV-Beginn 05.10.2022
Zeit und Ort
LV-Beschreibung
Intendierte Lernergebnisse
Students will successfully apply various tools from the qualitative theory of dynamical systems in order to understand models describing time-varying problems.
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, Hartman-Grobman theorem
Continuous dynamical systems: Lyapunov functions, planar equations (planar linear equations, Poincaré-Bendixson theory, closed orbits), stability
Erwartete Vorkenntnisse
Analysis, Linear Algebra, Ordinary Differential Equations
Prüfungsinformationen
Prüfungsmethode/n
Written exam
Prüfungsinhalt/e
Contents of the course
Beurteilungskriterien/-maßstäbe
50% of the obtained points are sufficient to pass the exam
Beurteilungsschema
Note BenotungsschemaPosition im Curriculum
- Masterstudium Mathematics
(SKZ: 401, Version: 18W.1)
-
Fach: Applied Analysis
(Wahlfach)
-
4.1 Dynamical Systems 1 (
2.0h VO / 4.0 ECTS)
- 312.106 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: 22W.1)
-
Fach: Analysis
(Pflichtfach)
-
1.1 Dynamical Systems 1 (
2.0h VO / 3.0 ECTS)
- 312.106 Dynamical Systems 1 (2.0h VO / 3.0 ECTS) Absolvierung im 1. Semester empfohlen
-
1.1 Dynamical Systems 1 (
2.0h VO / 3.0 ECTS)
-
Fach: Analysis
(Pflichtfach)
Gleichwertige Lehrveranstaltungen im Sinne der Prüfungsantrittszählung
-
Wintersemester 2023/24
- 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 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)