Complex Analysis (Summer 2019)

Contents

Analysis of functions of one complex variable: holomorphic functions, Möbius transformations, power series, Cauchy's integral theorem, zeros and singularieties, meromorphic functions, Laurent series, analytic continuation, residues, Riemann mapping theorem, partial fraction decomposition.

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

News

[17.09.2019]

Further exams on October 21 and October 23.
You can register at the office of Kati Gabler, MA873.

[31.07.2019]

The topics relevant for examination are everything until (and including) the Riemann mapping theorem.
This excludes elliptic functions.

[12.06.2019]

Exams are set for August 05 and August 02.
You can register at the office of Kati Gabler, MA873.

[04.06.2019]

There will be 10 exercise sheets with a total number of 210 points.

[22.05.2019]

Because of the holiday on May 30 the 6th exericse sheet will be due June 06, one week later,
and contain six exercises with a total of 30 points.

[02.04.2019]

First lecture on Tuesday, April 08.
First tutorial on Thursday, April 18.

Exercise sheets

• exercise sheet 01, due April 25
• exercise sheet 02, due May 02
• exercise sheet 03, due May 09
• exercise sheet 04, due May 16
• exercise sheet 05, due May 23
• exercise sheet 06, due June 06
• exercise sheet 07, due June 13
• exercise sheet 08, due June 20
• exercise sheet 09, due June 27
• exercise sheet 10, due July 04

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.
• Your hand-ins have to be STAPLED TOGETHER and contain names and matriculation numbers of all members of the group.
  We strongly reccommend you to hand in the homework in readable writing, since unreadable writing will not be corrected.
• The homeworks are due weekly on Thursday before(!) the start of the lecture.

Literature

• Alexander Bobenko, lecture notes
• Dirk Ferus, lecture notes
• Jänich, Funktionentheorie. Eine Einführung.
• Ahlfors, Complex Analysis.
• Lang, Complex Analysis.
• Needham, Visual Complex Analysis (also translated as: Anschauliche Funktionentheorie.)

Office hours