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Complex Analysis (Summer 2016)
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Contents
Analysis of one complex variable: holomorphic functions, Möbius transformations, Cauchy's integral
theorem, analytical continuation, residues, partial fraction decomposition, Riemann mapping theorem
This is a course of the Berlin Mathematical School
held in english or deutsch (depending on the audience).
News
- [2016, July 18]
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Somebody accidentally handed in a corrected exercise sheet
of something that looks like Financial Mathematics.
It is signed by M.V.
- [2016, July 18]
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There is now a Bonus Exercise Sheet online
which you may hand in together with Exercise Sheet 12 on Thursday, July
21.
- [2016, July 18]
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Corrected hint in Exercise Sheet 12, Exercise 2.
- [2016, July 07]
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Exercise Sheet 10, Exercise 2: $\varphi(0)$ does not have to be $0$.
One may drop this condition and define the winding number by
$\nu(\gamma, 0) = \frac{\varphi(1) - \varphi(0)}{2\pi}$.
- [2016, July 04]
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There will be a total number of 12 exercise sheets for this course
with a sum of 240 regular points.
- [2016, May 17]
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Sheet 3, Exercise 3 (ii): All $\varphi$ and $\phi$ should be the same,
as they are now.
- [2016, May 09]
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The Tuesdays tutorial is now moved to Wednesday, 16-18, MA 850,
starting this week.
- [2016, April 28]
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Additional tutorial on Wednesday, May 04, 16-18, MA 850.
- [2016, April 27]
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Deadline for exercise sheet 01 is extended till May 09.
- [2016, April 07]
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First lecture on Monday, April 18.
First tutorials in the second week.
Exercise sheets
- bonus sheet, due July 21
- exercise sheet 12, due July 21
- exercise sheet 11, due July 14
- exercise sheet 10, due July 07
- exercise sheet 09, due June 30
- exercise sheet 08, due June 23
- exercise sheet 07, due June 16
- exercise sheet 06, due June 09
- exercise sheet 05, due June 02
- exercise sheet 04, due May 26
- exercise sheet 03, due May 19
- exercise sheet 02, due May 12
- exercise sheet 01, due May 09
Homework policy
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To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments.
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The exercises are to be solved in groups of two people.
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The homeworks are due weekly at the beginning of the lecture on Monday. Late homeworks are accepted only with medical excuse.
Literature
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Alexander
Bobenko's lecture notes
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Dirk
Ferus' lecture notes (also contains a list of more good books)
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Ahlfors, Complex Analysis.
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Jänich, Funktionentheorie. Eine Einführung.
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Needham, Visual Complex Analysis. (also translated as: Anschauliche Funktionentheorie.)
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... and countless other good books
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