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Complex Analysis II (Winter 2014/15)


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 SchwarzChristoffel 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 9.3011.30 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, 1214, 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 1216) 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. PrenticeHall,
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. McGrawHill, 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
