Universität Wien

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

2.00 ECTS (1.00 SWS), SPL 25 - Mathematik
Prüfungsimmanente Lehrveranstaltung
VOR-ORT
Moodle
Fr 31.05. 11:30-13:00 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").

Details

max. 25 Teilnehmer*innen
Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

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.

Mindestanforderungen und Beurteilungsmaßstab

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.

Prüfungsstoff

Exercises will be set (available online) during the course.

Literatur

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)

Zuordnung im Vorlesungsverzeichnis

MBIV; MSTS; MANS

Letzte Änderung: Mi 28.02.2024 10:26