312.100 (19W) Dynamical Systems 1
Overview
- Lecturer
- Course title german Dynamical Systems 1
- Type Lecture
- Hours per Week 2.0
- ECTS credits 4.0
- Registrations 5
- Organisational unit
- Language of instruction English
- possible language(s) of the assessment English
- Course begins on 02.10.2019
- eLearning Go to Moodle course
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, Hartman-Grobman theorem
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. We will agree on the details on the first week.
Examination topic(s)
Definitions, theorems, examples, proofs.
Assessment criteria / Standards of assessment for examinations
50% of the points are sufficient in order to pass the exam.
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 VO / 4.0 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)
- Masterstudium Mathematics
(SKZ: 401, Version: 18W.1)
-
Subject: Applied Analysis
(Compulsory elective)
-
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)
-
Subject: Applied Analysis
(Compulsory elective)
- Masterstudium Mathematics
(SKZ: 401, Version: 18W.1)
-
Subject: Applied Mathematics
(Compulsory elective)
-
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)
-
Subject: Applied Mathematics
(Compulsory elective)
- 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 VO / 4.0 ECTS)
-
Dynamische Systeme 1 (
2.0h VU / 3.0 ECTS)
-
Subject: Analysis
(Compulsory subject)
- Doctoral programme Doctoral programme in Technical Sciences
(SKZ: 786, Version: 12W.4)
-
Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Compulsory subject)
-
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)
-
Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Compulsory subject)
Equivalent courses for counting the examination attempts
-
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)