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Complex Analysis I (Summer 2017) Komplexe Analysis I
Growing summary of contents
Analysis of one complex variable: holomorphic functions, line integrals, Cauchy's integral
theorem, singularities, residues, Laurent series, partial fraction decomposition, analytic continuation, Möbius transformations, Riemann mapping theorem, ...
Prerequisites are the contents of the courses Analysis I and II (single- and multivariable calculus) and Linear Algebra. It might be especially helpful to review power series of one variable.
This is an Additional Basic Course of the Berlin Mathematical School
held in English or German (depending on the audience).
Note that Monday, May 01, Thursday, May 25 and Monday, June 05 are public holidays, so there will be neither lectures nor tutorials on these days.
- [2017, Apr 24]
There was a typo in Exercise 2 of Sheet 1. Please check out the corrected version!
- [2017, Feb 06]
First lecture on Thursday, April 20.
First tutorials in the second week.
To get a certificate for the tutorial, you need to satisfactorily complete 50% of the homework assignments. This is required for taking the final exam ('Modulprüfung').
The exercises are to be solved in groups of two people.
The homework is due weekly at the beginning of the lecture on Thursday. Late homework is only accepted with a medical excuse.
Bobenko's lecture notes (in German)
Dirk Ferus' lecture notes (mostly in German, also contains a list of more good books)
Ahlfors, Complex Analysis.
Jänich, Funktionentheorie – Eine Einführung. (in German)
Needham, Visual Complex Analysis, also translated as: Anschauliche Funktionentheorie.
- Wegert, Visual Complex Functions – An Introduction with Phase Portraits.
- Conway, Functions of One Complex Variable.
- Freitag/Busam, Funktionentheorie 1. (in German)
- Behnke/Sommer: Theorie der analytischen Funktionen einer komplexen Veränderlichen. (in German)
... and countless other good books.
Ferus' lecture notes also mention the following writings on the history of the subject:
- Klein, Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert. (in German)
- Gaier, Über die Entwicklung der Funktionentheorie in Deutschland von 1890 bis
1950. In: Ein Jahrhundert Mathematik 1890-1990. Festschrift zum Jubiläum der DMV. (in German)
There is a book collection ("Semesterapparat") for this course in the Mathematics Library on the first floor.