Universität Wien

250010 PS Introductory Seminar on Dynamical System and Nonlinear Differential Equations (2024S)

2.00 ECTS (1.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
ON-SITE
Moodle
Fr 31.05. 11:30-13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

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).

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

Friday 08.03. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Friday 22.03. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Friday 19.04. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Friday 03.05. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Friday 17.05. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Friday 14.06. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
Friday 28.06. 11:30 - 13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

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

In the proseminar, we practise 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

The assessment is based on performance at the board during the proseminar, and completing (tick-list used) at least two thirds of the set exercises.

Minimum requirements and assessment criteria

The assessment is based on performance at the board during the proseminar, and completing (tick-list used) at least two thirds of the set exercises.

Examination topics

Exercises will be set (available online) 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

MBIV; MSTS; MANS

Last modified: We 28.02.2024 10:26