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Nonlinear Dynamics

Module MA3082

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2011/2

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2017/8SS 2012WS 2011/2

Basic Information

MA3082 is a semester module in English language at Bachelor’s level which is offered in winter semester.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions

Content

Elements of phase space analysis: equilibria, periodic orbits, concepts of stability, invariant sets, local vs global dynamics. Linearization. Poincaré-Bendixon theory. Steady state bifurcations: Fold, Hopf. Perturbation theory, asymptotics, averaging. Examples of chaotic dynamics: one-dimensional maps, three-dimensional flows; basics of symbolic dynamics. Applications (from engineering, natural sciences, etc.)

Learning Outcome

Nach dem erfolgreichen Abschluss des Moduls sind die Studierenden in der Lage, die grundlegende mathematische Theorie endlich-dimensionaler kontinuierlicher sowie diskreter dynamischer Systeme zu verstehen und deren analytische Behandlung zu beherrschen. Sie sind vertraut mit der Nutzung relevanter Software.

Preconditions

MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2, MA2004 Vector Analysis, MA2005 Ordinary Differential Equations

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.

Media

blackboard

Literature

Wiggins, Stephen: Introduction to Applied Nonlinear Dynamical Systems and Chaos; Springer-Verlag, New York 1990.
Chow, S.-N./Hale, J. K.: Methods of Bifurcation Theory; Springer-Verlag, New York 1995.

Module Exam

Description of exams and course work

The module examination is based on a written exam (60 minutes). For the exam students have to know basic concepts and methods of the mathematical theory of nonlinear dynamical systems and can apply them adequately and with mathematical precision to problems of this field.

Exam Repetition

The exam may be repeated at the end of the semester.

Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
TimeLocationInfoRegistration
Introduction to Nonlinear Dynamics
Thu, 2021-02-18, 14:15 till 15:15 Written electronic remote exam with video surveillance till 2021-01-15 (cancelation of registration till 2021-02-11)
Thu, 2021-04-08, 11:30 till 12:30 Written electronic remote exam with video surveillance till 2021-03-22 (cancelation of registration till 2021-04-01)
Introduction to Nonlinear Dynamics
Thu, 2021-02-18, 14:15 till 15:15 0.002
Written electronic remote exam on site option; We ask that you read the information below carefully and register for the examination only if you intend to take it under the specified conditions https://www.tum.de/en/about-tum/news/coronavirus/corona-teaching-exams/: You are not permitted to take part in the examination if you are subject to quarantine pursuant to the current Entry Quarantine Ordinance, if you have had contact with someone infected with COVID-19, or if you exhibit symptoms on the day of the examination. If you belong to a risk group and are thus subject to a severe progression of the illness, you are required to take the necessary measures for your own protection if you plan to take part in the examination, or to refrain from participating. The TUM Corona Crisis Task Force (krisenstab-coronavirus@tum.de) or your attending physician can advise you in this regard. till 2021-01-15 (cancelation of registration till 2021-02-11)
Thu, 2021-04-08, 11:30 till 12:30 Interims I: 101
Written electronic remote exam on site option; We ask that you read the information below carefully and register for the examination only if you intend to take it under the specified conditions https://www.tum.de/en/about-tum/news/coronavirus/corona-teaching-exams/: You are not permitted to take part in the examination if you are subject to quarantine pursuant to the current Entry Quarantine Ordinance, if you have had contact with someone infected with COVID-19, or if you exhibit symptoms on the day of the examination. If you belong to a risk group and are thus subject to a severe progression of the illness, you are required to take the necessary measures for your own protection if you plan to take part in the examination, or to refrain from participating. The TUM Corona Crisis Task Force (krisenstab-coronavirus@tum.de) or your attending physician can advise you in this regard. till 2021-03-22 (cancelation of registration till 2021-04-01)
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