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Complex Analysis II

       

  

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Complex Analysis II (Winter 2017/2018)

Lectures Yuri Suris Mon 10-12 MA 650
Wed 10-12
MA 744
Tutorial Ulrike Bücking Mon 12-14 MA 650

Contents

Conformal mappings, Elliptic functions, Analytic theory of differential equations

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

News

[30.11.2017]
Keine Sprechstunde von Ulrike Bücking am Donnerstag, den 14.12.17. Bitte einen anderen Termin vereinbaren oder per Email Fragen stellen.
[13.11.2017]
Ergänzung zu Normalteilern und Faktorgruppen kann man in Büchern zur Algebra finden, z.B. online über die UB in Karpfinger, Meyberg (Abschnitte 4.1 und 4.3).
[23.10.2017]
No lecture on Wednesday 25.10.17 and Wednesday 1.11.17. But there will be a lecture on Monday, 30.10.17.
Instead, there will be two lectures on Friday, 3.11.17, 10-14 h in MA 544.
New bigger room MA 650 for the tutorial starting on Monday, 30.10.17.
[18.10.2017]
Updated version of the first exercise sheet correcting a typo in 1d) and containing additional hints to 3a).
[1.10.2017]
First lecture on Monday, October 16.
There will also be a (short) tutorial on Monday, October 16, after the lecture containing some revision from Complex Analysis I.
Tutorials for the new content start in the second week.

Exercise sheets

Every week there will be a new exercise sheet on this page (usually on Friday).

Homework policy

  • The exercises are to be solved individually or in groups of two people.
  • The exercise sheets are to be handed in at the beginning of the tutorial.
  • To get a certificate for the tutorial, you need to satisfactorily complete 60% 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.
  • Ovsienko and Tabachnikov What is ... the Schwarzian Derivative?

There are many textbooks on complex analysis covering some part of the material of this cours, including all languages and some old volumes. Here is some additional literature.

  • Lang. Complex Analysis. Springer, several editions.
  • Kyrala. Applied Functions of a complex variable. Wiley, 1972.
  • Lorenz. Funktionentheorie. Spectrum Verlag, 1997, in German.
  • Moretti. Functions of a complex variable. Prentice-Hall, 1964.
  • Priwalow. Einführung in die Funktionentheorie. Teil III. Teubner, 1959, in German.
  • Tutschke and Vasudeva. An introduction to complex analysis. Chapman and Hall, 2005.
  • Hille. Ordinary differential equations in the complex domain. Wiley, 1976.
  • Plemelj. Problems in the sense of Riemann and Klein. Interscience, 1964.
  • Gray. Linear differential equations and group theory from Riemann to Poincaré. Birkhäuser, 1986.
  • Klein. Vorlesungen über die hypergeometrische Funktion. Springer, several editions, in German.
  • Kratzer and Franz. Transzendente Funktionen. AVG, 1960, in German.
There is also further literature containing elliptic function theory, for example by Valiron, Saks and Zygmund, Neville, Chandraskharan....

Some further textbooks covering mostly Complex Analysis 1:

  • Jänich. Funktionentheorie: Eine Einführung. Springer, several editions, in German.
  • Ahlfors. Complex Analysis. McGraw-Hill, several editions.
  • Fischer and Lieb. A Course in Complex Analysis. Springer, 2011.
  • Remmert. Funktionentheorie. Band 1 und 2. Springer, several editions, in German.

Office hours

Yuri Suris Wed 14-15 MA 827
Ulrike Bücking Thu 13-14 MA 864

Ulrike Buecking . 13.12.2017.