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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 1416 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
