Universität Wien
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250064 VO Advanced complex analysis (2023W)

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

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

I will attend a conference from Oct. 8-13, there will be no lectures and no proseminar. I will try to make up at least one of the lectures later.

  • Tuesday 03.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 06.10. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 17.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 20.10. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 31.10. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 03.11. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 07.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 14.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 17.11. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 28.11. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 01.12. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.12. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 12.12. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 15.12. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 16.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Friday 19.01. 09:45 - 11:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 30.01. 09:45 - 11:15 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

The course is a continuation of the bachelor course on complex analysis and will treat advanced topics that are part of the classical material in complex analysis.
Topics include but are not limited to: general versions of Cauchy's theorem, homology, homotopy, residue calculus, theorems of Weierstrass, Mittag-Leffler, approximation theorem of Runge, Riemann mapping theorem, entire functions, analytic continuation.

The selection of material will depend on the prior knowledge of students. Some of the necessary background will be recapitulated at the beginning of the course.

Prerequisites: analytic functions and their characterization, line integrals and simple versions of Cauchy's integral theorem, residue theorem, singularities, Laurent series (see lecture notes of Markus Fulmek).

Assessment and permitted materials

Oral exam on entire course material

Minimum requirements and assessment criteria

Satisfactory answer of questions about course and solution of problems.
To pass, at least half of the questions need to be answered correctly.
Theoretical list of grades:
88-100 sehr gut
75-87 gut
62-74 befriedigend
50-61 genuegend
<50 nicht genuegend

Examination topics

Entire course material

Reading list

John B. Conway, Functions of one complex variable I
L. Ahlfors, Complex analysis
B. Simon, Basic complex analysis
R. Remmert. Complex analysis
W. Rudin, Real and complex analysis
E. Stein, R. Shakarchi, Princeton Lectures on Analysis, Vol. 2

Association in the course directory

MANK

Last modified: We 25.09.2024 12:06