Complex Analysis II (Winter 2015/2016)

Contents

Elliptic functions, Conformal mapping, Analytic theory of differential equations

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

News

[09.02.2016]

There will be no tutorial on February 10.
The last tutorial will be on February 11.

[01.02.2016]

Exams can be taken on February 18.
Another date will be in April.

[27.01.2016]

The last exercise sheet is online (number 12).
The total number of regular points is 235.

[06.01.2016]

No tutorials on January 13 and 14.
Exercise Sheet 10 is therefore due January 21.
You can obtain 30 points on this sheet, 10 of which are bonus.

[04.01.2016]

New office of Jan Techter is MA883.

[05.12.2015]

Correction Sheet 7, Exercise 3: Some squares are missing:
The differential equations in (i) and (ii) are supposed to read $\dot{v}^2 = \dots$ and $\dot{u}^2 = \dots$ as you have already seen in the tutorial.

[02.12.2015]

Correction Sheet 6, Exercise 1:
The function $\mu:U_2 \rightarrow U_1$ is not necessarily biholomorphic, but in general only holomorphic.

[26.11.2015]

The differential you are supposed to consider in Sheet 6, Exercise 2 (i) is $\frac{d\lambda}{\mu}$.

[24.11.2015]

Correction Sheet 4, Exercise 3 (v):
It has to be $\Gamma_0[2] = \Gamma[2] \cup \Gamma[2]\cdot T_1$.
You got the points for detecting the error in this case.

[18.11.2015]

Correction in equation (3) of Exercise Sheet 5.

[17.11.2015]

No lecture on Monday, November 23.

[29.10.2015]

Note on Exercise Sheet 02 Exercise 4: Of course $f$ is supposed to be holomorphic away from singularities.

[29.10.2015]

You may hand in Exercise 4 of Exercise Sheet 02 one week later, together with Exercise Sheet 03.

[26.10.2015]

Slight correction on Exercise Sheet 01, Exercise 3 (ii) and (iii), making them a bit more precise:
It is now stated that there are no more poles than the previously given ones.

[26.10.2015]

The Thusday tutorial is now at 14-16 in room MA742.

[10.10.2015]

First lecture on Monday, October 12.
No lecture on Tuesday, October 13.
First tutorials in the second week.

Exercise sheets

• exercise sheet 12, due February 04
• exercise sheet 11, due January 28
• exercise sheet 10, due January 21
• exercise sheet 09, due January 07
• exercise sheet 08, due December 17
• exercise sheet 07, due December 10
• exercise sheet 06, due December 03
• exercise sheet 05, due November 26
• exercise sheet 04, due November 19
• exercise sheet 03, due November 12
• exercise sheet 02, due November 05
• exercise sheet 01, due October 29

Homework policy

• The exercises are to be solved in groups of two people.
• The exercise sheets will usually be online on Tuesdays.
  They are to be handed in at the beginning of the tutorial, one week later.
• To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.

Literature

• Hurwitz and Courant. Funktionentheorie.
  This book is not in copyright anymore and can be viewed here.
  It contains the following book (which was reprinted by Springer) as a chapter.
• Hurwitz. Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen.
• Fischer and Lieb. Funktionentheorie.
• Ahlfors, Complex Analysis.
• Whittaker and Watson. A course of modern analysis.
• Golubew. Vorlesungen über Differentialgleichungen im Komplexen.
• Ince. Ordinary differential equations.

Office hours