Fakultät II
Institut für Mathematik

# Complex Analysis

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# Complex Analysis (Summer 2016)

 Lectures Tutorials Boris Springborn Mon 16-18 MA 144 Thu 16-18 MA 144 Jan Techter Wed 16-18 MA 850 Thu 10-12 MA 549

### Contents

Analysis of one complex variable: holomorphic functions, Möbius transformations, Cauchy's integral theorem, analytical continuation, residues, partial fraction decomposition, Riemann mapping theorem

This is a course of the Berlin Mathematical School held in english or deutsch (depending on the audience).

### News

[2016, July 18]
Somebody accidentally handed in a corrected exercise sheet of something that looks like Financial Mathematics. It is signed by M.V.
[2016, July 18]
There is now a Bonus Exercise Sheet online which you may hand in together with Exercise Sheet 12 on Thursday, July 21.
[2016, July 18]
Corrected hint in Exercise Sheet 12, Exercise 2.
[2016, July 07]
Exercise Sheet 10, Exercise 2: $\varphi(0)$ does not have to be $0$.
One may drop this condition and define the winding number by $\nu(\gamma, 0) = \frac{\varphi(1) - \varphi(0)}{2\pi}$.
[2016, July 04]
There will be a total number of 12 exercise sheets for this course with a sum of 240 regular points.
[2016, May 17]
Sheet 3, Exercise 3 (ii): All $\varphi$ and $\phi$ should be the same, as they are now.
[2016, May 09]
The Tuesdays tutorial is now moved to Wednesday, 16-18, MA 850,
starting this week.
[2016, April 28]
Additional tutorial on Wednesday, May 04, 16-18, MA 850.
[2016, April 27]
Deadline for exercise sheet 01 is extended till May 09.
[2016, April 07]
First lecture on Monday, April 18.
First tutorials in the second week.

### Homework policy

• To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.
• The exercises are to be solved in groups of two people.
• The homeworks are due weekly at the beginning of the lecture on Monday. Late homeworks are accepted only with medical excuse.

### Literature

• Alexander Bobenko's lecture notes
• Dirk Ferus' lecture notes (also contains a list of more good books)
• Ahlfors, Complex Analysis.
• Jänich, Funktionentheorie. Eine Einführung.
• Needham, Visual Complex Analysis. (also translated as: Anschauliche Funktionentheorie.)
• ... and countless other good books

### Office hours

 Boris Springborn see homepage MA 871 Jan Techter Thu 12-13 MA 883

 Jan Techter . 18.07.2016.