Universität Wien

250064 VO Advanced complex analysis (2016W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 06.10. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 07.10. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 13.10. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 14.10. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 20.10. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 21.10. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.10. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 28.10. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.11. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 04.11. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.11. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 11.11. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.11. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 18.11. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.11. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 25.11. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 01.12. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 02.12. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 09.12. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 15.12. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 16.12. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.01. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 13.01. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 19.01. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 20.01. 09:45 - 10:30 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 26.01. 09:45 - 11:15 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Friday 27.01. 09:45 - 10:30 Seminarraum 7 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 examination

Minimum requirements and assessment criteria

Positive examination

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