Complex Analysis (Summer 2013)

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

Contents

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

News

[12.07.2013]

An overview of the covered topics

[26.06.2013]

Solution to exercise 9.2

[02.05.2013]

Möbius transformations revealed

[30.04.2013]

There was a typo in exercise 1.b) of sheet 3: The left hand side of the equation to be proven has to be |a-c| |d-b|

[26.04.2013]

Next week, due to the holiday on the 1st of May, there will be no tutorial on Wednesday. Therefore, the tutorial on Thursday the 2nd will be held in Mar 0016, the new building at Marchstrasse, so that there is enough space for everybody who wants to attend.
Since, the week after, Thursday the 9th of May is also a holiday, the Wednesday tutorial on the 8th of May will be moved to H 2038 in the main building.

[26.04.2013]

In exercise 1.c) of the second sheet one should assume that a is not equal to 0

[18.04.2013]

A way of visualizing holomorphic functions.

[17.04.2013]

Please sign up here for the course.

[14.03.2013]

The first lecture will be on Monday 8.4.
The tutuorials will start on Wednesday 17.4.

Exercise sheets

The exercise sheets can be found here.

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 Tuesday. Late homeworks are accepted only with medical excuse.

Examinations

There will be oral examns at the end of the semester.

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.

There is a book collection ("Semesterapparat") for this course in the Mathematics Library on the first floor.

Office hours