Universität Wien

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

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

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Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

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.)

Mindestanforderungen und Beurteilungsmaßstab

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

Prüfungsstoff

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

MANO; MBIO; MSTO

Letzte Änderung: Fr 15.11.2024 12:06