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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

Lecture Notes