Universität Wien

250115 VO Dynamical Systems and Nonlinear Differential Equations (2024S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Register/Deregister for this course

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Friday 01.03. 11:30 - 13:00 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
  • Tuesday 05.03. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Friday 15.03. 11:30 - 13:00 Seminarraum 15, Kolingasse 14-16, OG01
  • Tuesday 19.03. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Tuesday 09.04. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Friday 12.04. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.04. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Tuesday 23.04. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Friday 26.04. 11:30 - 13:00 Seminarraum 15, Kolingasse 14-16, OG01
  • Tuesday 30.04. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Tuesday 07.05. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Friday 10.05. 11:30 - 13:00 Seminarraum 15, Kolingasse 14-16, OG01
  • Tuesday 14.05. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Tuesday 21.05. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Friday 24.05. 11:30 - 13:00 Seminarraum 15, Kolingasse 14-16, OG01
  • Tuesday 28.05. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Tuesday 04.06. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Friday 07.06. 11:30 - 13:00 Seminarraum 15, Kolingasse 14-16, OG01
  • Tuesday 11.06. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Tuesday 18.06. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01
  • Friday 21.06. 11:30 - 13:00 Seminarraum 15, Kolingasse 14-16, OG01
  • Tuesday 25.06. 16:45 - 18:15 Seminarraum 8, Kolingasse 14-16, OG01

Information

Aims, contents and method of the course

The aim of this lecture course is for the participants to obtain an understanding and a working knowledge of basic concepts and examples of Dynamical System and Nonlinear Differential Equations.

This course introduces and discusses aspects of both continuous and discrete dynamical systems, plus illustrative examples from applications. Specific topics include: flows; stability of fixed points (linearisation, Lyapunov functions); planar systems; bifurcation theory; notions of topological dynamics, attractors, and chaos, horseshoes, Poincare maps; further topics.

Prerequisites: Completion of a course on ordinary differential equations.

Assessment and permitted materials

Written exam

Minimum requirements and assessment criteria: sufficient understanding of the material discussed during the lectures
Prerequisites: Completion of a course on ordinary differential equations.

As usual, the final exam requires participants to demonstrate an understanding of the underlying theory and the ability to apply the results presented in the lectures. (Further information will be provided during the course.)

Minimum requirements and assessment criteria

The exam will indicate the points assigned to each question. Roughly half of the points are required to get a positive grade.

Examination topics

The contents of the course (outlined above). (Further information will be provided during the course.)

Reading list

Reading list: Textbooks related to this course include the following. (Further information will be provided during the course.)

R J Brown: A Modern Introduction to Dynamical Systems, Oxford University Press 2018,
(https://global.oup.com/academic/product/a-modern-introduction-to-dynamical-systems-9780198743286)

C Robinson: An Introduction to Dynamical Systems, 2nd ed, AMS 2012
(https://bookstore.ams.org/view?ProductCode=AMSTEXT/19)

S Strogatz: Nonlinear dynamics and chaos, with applications to physics, biology and engineering,
CRC Press, 2015, ISBN-13: 978-0813349107 or ISBN-10: 0813349109

G Teschl: Ordinary Differential Equations and Dynamical Systems, AMS Graduate Studies in Mathematics
(https://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf)

M Viana, J M Espinar: Differential Equations: A Dynamical Systems Approach to Theory and Practice,
AMS 2021 (https://bookstore.ams.org/view?ProductCode=GSM/212)

Association in the course directory

MANO; MBIO; MSTO

Last modified: Fr 15.11.2024 12:06