Universität Wien
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250096 VO Analysis on manifolds (2019S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Please note that we are only starting in the second week of the semester.

  • Monday 11.03. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.03. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.03. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 21.03. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 25.03. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.03. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 01.04. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 04.04. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.04. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 11.04. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.04. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 02.05. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.05. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.05. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.05. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.05. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.05. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.05. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.05. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 03.06. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 06.06. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 13.06. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.06. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.06. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.06. 15:00 - 16:30 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

I expect you to have a good grasp of multivariable calculus and linear algebra, including the inverse and inverse function theorem, basic point set topology, and multilinear maps on finite dimensional vector spaces.

— Geometry of charts in Euclidean space (this may be mostly review)

— Abstract manifolds and the gluing lemma

— Tangent bundle and its universal property

— Maps between manifolds and their associated tangent maps

— Special types of maps and their canonical forms

— Whitney embedding theorem

— Action of tangent fields on functions

— Lie bracket

— Vector bundles and the fundamental principle of tensor calculus

— Differential forms and their calculus

— Integration on manifolds

— Stokes’ theorem

We will discuss further topics such as the following depending on the interests of the audience:

— Sard’s theorem

— Elements of de Rham co-homology

— Flows of tangent fields

— Frobenius theorem on integrable distributions

— Derivations on vector bundles

Assessment and permitted materials

A thorough, half-hour exam.

Minimum requirements and assessment criteria

Examination topics

All course content is examinable.

Reading list

Lecture notes will be made available for large portions of the course material.

Association in the course directory

MGED

Last modified: Sa 20.03.2021 00:24