Funktionentheorie

This course will be presented based on the knowledge of the Bachelor course "Elemente der Funktionentheorie". Besides reminding some basic results of complex analysis, we will cover the following topics:

  • Riemann sphere and spherical distance.
  • Partial complex differentiations, the complex Green-Gauss integral theorem and the general Cauchy integral theorem,
  • Residue theorem and its applications,
  • Conformal mappings, the Möbius transformations, Riemann's Mapping theorem,
  • Construct holomorphic and meromorphic functions via Mittag-Leffler's theorem, Weierstrass factorization theorem.
  • Special holomorphic and meromorphic functions: Gamma function, Riemann zeta function, elliptic functions.
  • Harmonic functions, boundary value problems.

Lecture Team

Lecturer: Prof. Dr. Friedmar Schulz
Exercise instructor: Dr. Kim-Hang Le

Extent

  • ECTS credits: 9
  • Hours per week: 4+2

Examination

No prerequisites are necessary for exam registration.

We offer two writting examinations (schriftliche prüfung), the first at the end of this winter semester and the second before the beginning of the next summer semester:

  • Monday, 05.03.2018         9:30-11:30      E20-He18
  • Monday, 26.03.2018         9:30-11:30      E20-He18


Times and Rooms

  • Lecture (starting on 17.10.17)
    • Tuesday 10:0012:00:           He18, E20
    • Wednesday 12:0014:00:      He18, E20
  • Exercises (starting on 27.10.17)
    • Friday 12:0014:00:          He18, E60

Please enroll in Moodle!

Exercise sheets

References

  • Reinhold Remmert: Funktionentheorie I/II
  • Tutschke, W., Vasudeva, H.L.: An Introduction to Complex Analysis, Chapman&Hall / CRC 
  • Freitag, E., Busam, R.: Funktionentheorie, Springer