Advanced Complex Analysis,
Winter term 2019/20
Place and Time
| Type: | Time: | Place: | Start: |
| Lecture (VO) 3 hrs. | Mon 8:00-9:45 Wed 8:00-8:45 |
HS13 (OMP1) | 2.10. |
| Tutorials (PS) 1 hr. | Wed 8:45-9:30 | HS13 (OMP1) | 9.10. |
Content
We will cover some advanced topics from complex analysis. In particular,
advanced aspects of the calculus of residues, the Riemann mapping theorem, Runge's approximation theorem.
I will follow the lecture notes by Armin Rainer available for download from the link below.
Proseminar
The following problems should be prepared:
- Problem Set 1 (due 9.10): Exercise 1,2,3 from [Rainer]
- Problem Set 2 (due 16.10): Problem 1 from the sheet and Exercises 4,5 from [Rainer]
- Problem Set 3 (due 23.10): Problem 2,3 from the sheet and Exercise 6 from [Rainer]
- Problem Set 4 (due 30.10): Problem 4 from the sheet and Exercise 7,8 from [Rainer]
- Problem Set 5 (due 6.11): Exercise 9,10,11 from [Rainer]
- Problem Set 6 (due 13.11): Exercise 12,13,14 from [Rainer]
- Problem Set 7 (due 20.11): Exercise 15,16,17 from [Rainer]
- Problem Set 8 (due 27.11): Exercise 18,19,20 from [Rainer]
- Problem Set 9 (due 4.12): Exercise 21,22,23 from [Rainer]
- Problem Set 10 (due 11.12): Exercise 24,26,27 from [Rainer]
- Problem Set 11 (due 8.1): Exercise 29,30,31,32 from [Rainer]
- Problem Set 12 (due 15.1): Exercise 34,35,36 from [Rainer]
- Problem Set 13 (due 22.1): Exercise 39,40,41 from [Rainer]
- Problem Set 14 (due 29.1): Exercise 42,46,47 from [Rainer]
Target audience
Module "Advanced Complex Analysis" in the Master's programme in Mathematics.
Assessment
The course assessment for the lecture (VO) will be via an oral examination at the end of
the course. The course assessment for the tutorials (PS) will be via
participation (solving/presenting assigned problems) during the seminar.
Literatur
Einige Lehrbücher:
Looking forward to seeing you, Gerald Teschl
- M. Ablowitz und A. Fokas, Complex Analysis, 2. Aufl, Cambridge UP, Cambridge, 2003.
- R. E. Greene und S. G. Krantz, Function Theory of One Complex Variable, 3rd ed., AMS, Providence, 2006.
- A. Rainer, Advanced Complex Analysis, Lecture notes, 2017.
- E. M. Stein und R. Shakarchi, Complex Analysis, Princeton UP, Princeton, 2003.
- W. Schlag, A Course in Complex Analysis and Riemann Surfaces, AMS, Providence, 2014.