Complex Analysis (Summer 2010)

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

Office hours

News

exams

There are still some slots for orals on the 19.10 available. Please contact me (Thilo) by email.

[08. 7.]

The scriptum has again been updated and the certificates are ready to be collected in my office on monday (I'm not in on friday). If you want to pass an oral exam in July you need to register at the Pruefungsamt with your certificate. The plan for next week is to meet on wednesday after the lecture to have some cake/ice cream at the Mathecafe instead of a tutorial. In thursday's tutorial I will finish my overview of Complex Analysis I (chp. 8-end).

[29. 6.]

Update in homework number 10.1.ii). I added an optional exercise 10.4. that can be used to solve 10.1.ii). If you need extra points you may also solve the optional exercise and hand it in next week - see updated sheet below. Sorry.

[15. 6.]

The scriptum has been updated, see link below. There is an english version of the proof of Artin's criterion available.

[26. 5.]

There is no office our of Thilo on 01.06. Since I was not here today, please hand in the homework next week in the lecture. Thank you.

[25. 5.]

No tutorial on Thursday 03.06. Next homework (n. 7) is due on 03.06., i.e. two weeks for this sheet. For the tutorial on Thu 27.05. I will try to find a replacement, because I'm not in Berlin (thilo).

[18. 5.]

No lecture on monday 24.05.10 because of public holiday.

[11. 5.]

No tutorial on Thursday 13.05.10 due to public holiday. Drop your homework at my office MA874 before monday 12h.

[28. 4.]

No lecture on Monday 03.05.10!

[26. 4.]

Notes on integration available online.

[12. 4.]

Weekly schedule changed heavily. See above!

Contents

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

Exercise sheets

• Sheet 1 due 22.04.10
• Sheet 2 due 29.04.10
• Sheet 3 due 06.05.10
• Sheet 4 due 13.05.10
• Sheet 5 due 20.05.10
• Sheet 6 due 27.05.10
• Sheet 7 due 10.06.10 (in two weeks)
• Sheet 8 due 17.06.10
• Sheet 9 due 24.06.10
• Sheet 10 due 01.07.10
• Sheet 11 due 08.07.10

Homework policy

To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.

The exercise sheets we be available online on Wednesday morning and are due in the tutorial the following week.

Literature

• Ahlfors: Complex Analysis.
• Lang: Complex Analysis.
• Jänich: Einführung in die Funktionentheorie.
• Skript