Universität Wien

250122 VO Selected topics in Differential Equations: Lie-Transformation Groups (2015S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 02.03. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 04.03. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.03. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 11.03. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.03. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 18.03. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.03. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 25.03. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.04. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 15.04. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.04. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 22.04. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.04. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 29.04. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.05. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 06.05. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.05. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 13.05. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.05. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 20.05. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.05. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 01.06. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 03.06. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.06. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 10.06. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.06. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 17.06. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.06. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 24.06. 16:00 - 17:30 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.06. 11:40 - 13:10 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

The lecture course will start out by providing a general introduction to the theory of Lie transformation groups. Based on this, our main topic will be the symmetry group analysis of differential equations. In this field, methods of the theory of Lie transformation groups are applied to the analysis of symmetry- and invariance properties of systems of partial differential equations. Sophus Lie himself was primarily motivated by such questions when he originally developed his theory of Lie groups. In addition we will also discuss symmetries of variational problems, a theory founded by Emmy Noether, which, in the form of the celebrated Noether theorems, has had a far-reaching impact on various branches of theoretical physics.

Prerequisites: Differential geometry 1, Lie groups (in the form of the standard courses offered at our Faculty).

Assessment and permitted materials

Oral exam.

Minimum requirements and assessment criteria

The lecture course is intended to provide an introduction to this active field of research, formulated in the modern language of differential geometry.

Examination topics

Reading list

Brickel, F., Clark, R.S., Differentiable Manifolds. An Introduction. Van Nostrand, 1970.
Olver, P.J., Applications of Lie Groups to Differential Equations, 2nd Ed., Springer 1998.

Association in the course directory

MGEV

Last modified: Mo 07.09.2020 15:40