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Course: Complex Function Theory 2

News

  • Beginning November 21, 2017, the exercise session will begin at 2:00 PM instead of 2:15 PM.
  • The oral exams will take place on Thursday, March 8 and Friday, March 9, 2018 in MI 02.10.038.

Organisation

  • Lecture (2 SWS)
    • Lecturer: PD Dr. Peter Massopust
    • Module number: MA5005
    • ECTS-Points: 5
    • Time: Tuesdays, 12:15 - 1:45 PM
    • Location: MI 02.10.011
  • Exercise Session (1 SWS)
    • Time: Tuesdays, 2:15 - 3:45 PM
    • Location: MI 00.13.009A
    • Begin: November 7, 2017 and then every other week.

Content

  • Meromorphic Functions on the Riemann Sphere
  • Holomorphic Extension and Elementary Transcendental Functions
  • Descriptive Riemann Surfaces
  • Homology and holomorphic Differential Forms
  • Infinite Products and the Weierstraß Product Theorem (classical and modern Version)
  • Mittag-Leffler Distributions (classical and modern Version)
  • Riemann Mapping Theorem
  • Introduction to Sheaves and Sheaf Cohomology

Literature

  • E. Peschl, Funktionentheorie, Band I, B.I. Hochschultaschenbücher, Mannheim
  • A. Dinghas, Einführung in die Cauchy-Weierstraßsche Funktionentheorie, B.I. Hochschultaschenbücher, Mannheim
  • R. Remmert, Funktionentheorie 2, Springer Lehrbuch, Springer Verlag
  • R. Greene und S. Krantz, Function Theory of One Complex Variable, Graduate Studies in Mathematics, Vol. 40, Providence, Rhode Island
  • G. Sansone und J. Gerretsen, Lectures on the Theory of Functions of One Complex Variable, P. Noordhoff Ltd., Groningen, The Netherlands (advanced)
  • J. B. Conway, Functions of One Complex Variable, 2nd ed., Springer Verlag (advanced)
  • S. Lang, Complex Analysis, 2nd ed., Springer Verlag (advanced)
  • C. Berenstein und R. Gay, Complex Variables: An Introduction, Springer Verlag (advanced)
  • G. Jones und D. Singerman, Complex Functions: An algebraic and geometric viewpoint, Cambridge University Press (advanced)
  • O. Forster, Lectures on Riemann Surfaces, Springer Verlag, 1981 (advanced)

Problem Sets

Problem Set 1
Problem Set 2
Problem Set 3
Problem Set 4
Problem Set 5
Problem Set 6
Problem Set 7
Problem Set 8
Problem Set 9
Hints to Exercises (German)

Lecture Notes

Oct 17, 2017
Oct 24, 2017
Nov 07, 2017
Nov 14, 2017
Nov 21, 2017
Nov 28, 2017
Dec 05, 2017
Dec 12, 2017
Dec 19, 2017
Jan 09, 2018
Jan 16, 2018
Jan 23, 2018
Jan 30, 2018
Feb 06, 2018