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Complex Analysis (Summer 2016)


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, 1618, MA 850,
starting this week.
 [2016, April 28]

Additional tutorial on Wednesday, May 04, 1618, 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.
Exercise sheets
 bonus sheet, due July 21
 exercise sheet 12, due July 21
 exercise sheet 11, due July 14
 exercise sheet 10, due July 07
 exercise sheet 09, due June 30
 exercise sheet 08, due June 23
 exercise sheet 07, due June 16
 exercise sheet 06, due June 09
 exercise sheet 05, due June 02
 exercise sheet 04, due May 26
 exercise sheet 03, due May 19
 exercise sheet 02, due May 12
 exercise sheet 01, due May 09
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
