312.114 (23S) Dynamical Systems 2
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 schemePosition 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)
-
4.2 Dynamical Systems 2 (
2.0h VO / 4.0 ECTS)
-
Subject: Applied Analysis
(Compulsory elective)
- 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
-
4.1 Dynamical Systems 2 (
2.0h VO / 4.0 ECTS)
-
Subject: Applied Analysis
(Compulsory elective)
- 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
-
7.1 Wahl von weiteren Lehrveranstaltungen aus den Vertiefungsfächern (
0.0h XX / 12.0 ECTS)
-
Subject: Applied Mathematics
(Compulsory elective)
Equivalent courses for counting the examination attempts
This course is not assigned to a sequence of equivalent courses