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Complex Analysis II (Winter 2014/15)

Lectures Yuri Suris Tue 12-14 MA 144
Thu 12-14 MA 376
Tutorial Ulrike Bücking Wed 12-14 MA 848
Mon 12-14 MA 545

This is a course of the Berlin Mathematical School held in English.

Contents

Further topics in analysis of one complex variable: conformal mappings, in particular reflection principles and Schwarz-Christoffel formula; introduction to the theory of elliptic functions and some applications; analytic theory of differential equations, in particular Fuchsian differential equations and hypergeometric differential equations.

News

[11.2.15]
The certificates (Übungsscheine) can be found at Mrs Downes' office in MA 701 (Mon,Tue,Thu,Fri 9.30-11.30 am). During the semester break office hours of Yuri Suris and Ulrike Bücking are by appointment (please write an email).
[3.2.15]
Please note that the last tutorial takes place on Wednesday, February 11th.
[14.1.15]
Please note the corrections on homework sheet 10 in exercise 1+2 g).
[16.12.14, 5.1.15]
Please note the corrections on homework sheet 9 in exercise 1 a). Now all signs and exponents are correct.
[15.12.14]
There will be no office hour of Ulrike Bücking on Friday, December 19th. Please make an appointment or write an email.
[27.11.14]
Handwritten lecture notes of Prof. Suris can be found below. Updates will follow as the lecture advances.
[24.11.14]
There will be no office hour of Ulrike Bücking on Friday, November 28th. You can ask questions on Thursday or Monday instead (8.30 am to 3.30 pm) or write an email.
[14.11.14]
Please note the correction on homework sheet 5 in exercise 1. All exponents were missing in the formula for g.
[21.10.14]
There will be no office hour of Ulrike Bücking on Friday, November 7th. You can ask questions on Thursday or Monday instead (8.30 am to 3.30 pm) or write an email.
[21.10.14]
Please note the new room for the lectures on Thursday: MA 376. Also note that there will be no lecture on Thursday, 23.10.14.
[20.10.14]
The tutorial on Monday is very small. You may consider to switch your tutorial from Wednesday to Monday.
[15.10.14]
Please note the correction in homework exercise 3 of the first sheet and the adjustment of the due date.
[14.10.14]
There will be a second tutorial on Monday, 12-14, in MA 545 covering the same topics as the tutorial on Wednesday before.
[1.10.14]
The lecture starts on Tuesday 14.10.
The first tutorial is on October 15. There will possibly be a second tutorial.

Homework policy

To get a certificate for the tutorial, you need to satisfactorily complete 60% of the homework assignments. Homeworks shall be prepared individually or in groups of two students. Homework should be handed in at the beginning of the tutorial.

Exercise sheets

Every week there will be a new exercise sheet on this page (on Tuesday at the latest).

Lecture notes

This is a collection of handwritten lecture notes of Prof. Suris. Note that the third part (Chapters 12-16) are in German.

Literature

There are many textbooks on complex analysis covering some part of the material of this cours, including all languages and some old volumes. The following choice is not ordered by any aspect.

  • Fischer and Lieb. Ausgewaehlte Kapitel aus der Funktionentheorie. Vieweg, 1988, in German.
  • Hurwitz. Funktionentheorie. Birkhäuser, 1932, in German.
  • Hurwitz. Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen. Springer, 2000, in German.
  • Golubew. Vorlesungen über Differentialgleichungen im Komplexen. Deutscher Verlag der Wissenschaften, 1958, in German.
  • Ince. Ordinary differential equations. Dover publications, 1926.
  • Whittaker and Watson. A course of modern analysis. Cambridge University Press, 1927.
  • 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. Funktionentheorie. Vieweg, several editions, in German.
  • Fischer and Lieb. A Course in Complex Analysis. Springer, 2011.
  • Remmert. Funktionentheorie. Band 1 und 2. Springer, several editions, in German.

Office hours

Office hours Yuri Suris Wed 14-15 and by appointment MA 827
Ulrike Bücking Fri 13-14 and by appointment MA 864

Ulrike Bücking . 06.05.2015.