312.114 (23S) Dynamical Systems 2

Sommersemester 2023

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First course session
06.03.2023 09:00 - 11:00 HS 7 On Campus
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Overview

Lecturer
Course title german Dynamical Systems 2
Type Lecture
Course model Attendance-based course
Hours per Week 2.0
ECTS credits 4.0
Registrations 7
Organisational unit
Language of instruction English
Course begins on 06.03.2023
eLearning Go to Moodle course

Time and place

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Course Information

Intended learning outcomes

To be able to analyze qualitative behavior of  dynamical systems using various notions and tools of  Nonlinear Dynamics and Stability Theory.

Teaching methodology

Lecture, discussion, examples

Course content

The course focuses on the study of dynamical systems governed by nonlinear ordinary differential equations. We will consider some fundamental concepts  of the theory of nonlinear dynamical systems and discuss their applications in areas ranging from
control theory and mechanics.

  The main topics are:

  • Elements of nonlinear ODEs 
  • Lyapunov stability  
  • Bifurcations
  • Center manifolds
  • Elements of dynamical control systems

Prior knowledge expected

Analysis, Linear Algebra, Ordinary Differential Equations

Literature

  • V.I. Arnold. Ordinary Differential Equations.
  • J. Guckenheimer, P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations
    of Vector Fields.
  • H. Khalil. Nonlinear Systems.
  • H. Nijmeijer , A. van der Schaft.  Nonlinear Dynamical Control Systems.
  • S. Sastry. Nonlinear Systems.

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 end-term exam.

Examination topic(s)

Contents of the course.

Assessment criteria / Standards of assessment for examinations

50% of the obtained points are sufficient to pass the exam.





Grading scheme

Grade / Grade grading scheme

Position in the curriculum

  • Master's degree programme Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Analysis (Compulsory elective)
      • 4.2 Dynamical Systems 2 ( 2.0h VO / 4.0 ECTS)
        • 312.114 Dynamical Systems 2 (2.0h VO / 4.0 ECTS)
  • Master's degree programme Mathematics (SKZ: 401, Version: 22W.1)
    • Subject: Applied Analysis (Compulsory elective)
      • 4.1 Dynamical Systems 2 ( 2.0h VO / 4.0 ECTS)
        • 312.114 Dynamical Systems 2 (2.0h VO / 4.0 ECTS)
          Absolvierung im 1., 2., 3. Semester empfohlen
  • Master's degree programme Mathematics (SKZ: 401, Version: 22W.1)
    • Subject: Applied Mathematics (Compulsory elective)
      • 7.1 Wahl von weiteren Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
        • 312.114 Dynamical Systems 2 (2.0h VO / 4.0 ECTS)
          Absolvierung im 2., 3. Semester empfohlen

Equivalent courses for counting the examination attempts

This course is not assigned to a sequence of equivalent courses