Universität Wien
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250029 VO Analysis 3 (2023S)

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

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Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 02.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.03. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.03. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.03. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.04. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 20.04. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.04. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.04. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 04.05. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.05. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 11.05. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.05. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.05. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 25.05. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 01.06. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 05.06. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.06. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 15.06. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.06. 11:30 - 13:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 22.06. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 29.06. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The course further develops analysis, in particular the theory of differentiation and integration in several variables. On the one hand, we will emphasize topological aspects of analysis, for which continuity of functions plays a key role. On the other hand, we will discuss geometrical aspects, an in particular identify subsets of R^n that are nice enough to allow for a geometrical study by analytical methods. The study of these so-called submanifolds will form the core of the course. An important topic will be integration over submanifolds, for which one first has to find the right objects to be integrated. This leads to differential forms which will be studied in detail and to a general version of Stokes' theorem, which generalizes the classical theorems of Green, Gauß and Stokes. These are fundamental for several parts of classical physics.

The prerequisites for the course include analysis in one dimension as well as in higher dimensions, in particular the module "Analysis 2" and multidimensional integrals as discussed in the module "Integration and Stochastics".

Assessment and permitted materials

Written or oral exam after the end of the course; no materials permitted.

Minimum requirements and assessment criteria

Understanding the key concepts, results and proofs on submanifolds of R^n and on differential and integral calculus on submanifolds. In written exams, at least half of the possible points have to be obtained to get a positive mark.

Examination topics

The contents of the lecture course.

Reading list

Written material for the course will be provided (in parts) in due time, in particular via the moodle page of the course. The topics of the course (in particular the analytical aspects) are treated in many textbooks for example in the following books (in German):
H. Amann, J. Escher: Analysis III (Springer, 2009)
O. Forster: Analysis 3 (Vieweg, 7. Auflage 2012)
H. Heuser: Analysis 2 (B. G. Teubner, 13. Auflage 2004)
K. Jänich: Vektoranalysis (Springer, 5. Auflage 2005)
K. Königsberger: Analysis 2 (Springer, 5. Auflage 2004)
W. Rudin: Analysis (Oldenbourg, 3. Auflage 2005)

Association in the course directory

AN3

Last modified: Th 01.02.2024 11:46