Universität Wien

250064 VO Advanced complex analysis (2017W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 02.10. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 03.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.10. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.10. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.10. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.10. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.11. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 07.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.11. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.11. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.11. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.12. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.12. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.12. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.12. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.01. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.01. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.01. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.01. 09:30 - 10:15 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The following topics will be presented:

- repetition of the residue calculus, Laurent series
- Runge’s theorem and its applications, the inhomogeneous Cauchy-Riemann equation, the Mittag-Leffler theorem, the Weierstrass factorization theorem
- the Riemann mapping theorem, characterization of simply connected regions, continuity at the boundary (Caratheodory’s theorem), biholomorphisms of annuli
- harmonic and subharmonic functions, the Schwarz reflection principle, Harnack’s principle, the Dirichlet Problem
- elliptic functions, the Weierstrass P-function, modular functions, the Picard theorems
- introduction to Riemann surfaces, analytic continuation, (branched) coverings

Assessment and permitted materials

Oral exam

Minimum requirements and assessment criteria

Knowledge and comprehension of the topic presented in the course.

Examination topics

Topics presented in the course.

Reading list

Lecture notes will be provided. Further reading:

- L. V. Ahlfors, Complex analysis: An introduction of the theory of analytic functions of one complex variable, Second edition, McGraw-Hill Book Co., New York-Toronto-London, 1966.

- L. V. Ahlfors and L. Sario, Riemann surfaces, Princeton Mathematical Series, No. 26, Princeton University Press, Princeton, N.J., 1960.

- H. Cartan, Elementary theory of analytic functions of one or several complex variables, Dover Publications, Inc., New York, 1995, Translated from the French, Reprint of the 1973 edition.

- J. B. Conway, Functions of one complex variable, second ed., Graduate Texts in Mathematics, vol. 11, Springer-Verlag, New York-Berlin, 1978.

- J. B. Conway, Functions of one complex variable. II, Graduate Texts in Mathematics, vol. 159, Springer-Verlag, New York, 1995.

- H. M. Farkas and I. Kra, Riemann surfaces, Graduate Texts in
Mathematics, vol. 71, Springer-Verlag, New York-Berlin, 1980.

- O. Forster, Lectures on Riemann surfaces, Graduate Texts in
Mathematics, vol. 81, Springer-Verlag, New York, 1991, Translated from the
1977 German original by Bruce Gilligan, Reprint of the 1981 English translation.

- R. E. Greene and S. G. Krantz, Function theory of one complex variable,
third ed., Graduate Studies in Mathematics, vol. 40, American Mathematical Society, Providence, RI, 2006.

- L.Hörmander, An introduction to complex analysis in several
variables, third ed., North-Holland Mathematical Library, vol. 7, North-Holland Publishing Co., Amsterdam, 1990.

- R. Narasimhan and Y. Nievergelt, Complex analysis in one variable, second ed., Birkhäuser Boston, Inc., Boston, MA, 2001.

- W. Rudin, Real and complex analysis, third ed., McGraw-Hill Book Co., New York, 1987.

- E. M. Stein and R. Shakarchi, Complex analysis, Princeton Lectures in Analysis, II, Princeton University Press, Princeton, NJ, 2003.

Association in the course directory

MANK

Last modified: Mo 07.09.2020 15:40