Fiches de cours

Topics in complex analysis

MATH-327

Enseignant(s) :

Ruf Matthias Benjamin

Langue:

English

Summary

The goal of this course is to treat selected topics in complex analysis. We will mostly focus on holomorphic functions in one variable. If time permits we will also introduce holomorphic functions in several variables.

Content

- Sequences of holomorphic functions

- Functions with prescribed principal part

- Infinite products

- Holomorphic functions with prescribed zeros

- The Riemann mapping theorem

 

- Picard's great theorem

- The Riemann sphere

- An introduction to holomorphic functions in several variables

Keywords

Complex analysis, Mittag-Leffler theorem, Weierstrass product theorem, Riemann mapping theorem, Picard's great theorem, several complex variables

Learning Prerequisites

Required courses

Analysis I-III (especially basic theory of holomorphic functions)

Important concepts to start the course

Basic theory of holomorphic functions in one complex variable

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

Lectures (on blackboard) and exercise sessions with assistant

Expected student activities

Attending the lectures, solving the exercises

Assessment methods

Written exam

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Office hours No
Assistants Yes
Forum Yes

Resources

Bibliography

R. Remmert: Classical topics in complex function theory. Springer, New York, 1998

C. Laurent-Thiébaut: Holomorphic function theory in several variables: an introduction, Springer, London, 2011

Notes/Handbook

There will be weekly lecture notes available in moodle.

Dans les plans d'études

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15MAA110    
15-16 MAA110  
16-17    
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand