312.100 (19W) Dynamical Systems 1

Wintersemester 2019/20

Registration deadline has expired.

First course session
02.10.2019 15:00 - 17:00 N.2.01 On Campus
... no further dates known

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

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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

Im Fall von online durchgeführten Prüfungen sind die Standards zu beachten, die die technischen Geräte der Studierenden erfüllen müssen, um an diesen Prüfungen teilnehmen zu können.

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 scheme

Position 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)
  • 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)
  • 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)
  • 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)
  • 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)

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)