OVERVIEW

The course introduces advanced topics in complex analysis.

AIMS AND CONTENT

LEARNING OUTCOMES

Advanced notions of functions of a complex variable, including: Gamma function, Rouche and Picard theorems, Riemann map theorem and main properties of order finished.

AIMS AND LEARNING OUTCOMES

At the end of the course the student will have to know the thory of entire functions of finite order, the theory of biolomorphisms and conformal maps on C, and the theory of special functions.

PREREQUISITES

The main prerequisite is the basic theory of complex analysis.

TEACHING METHODS

52 hours of frontal lectures.

SYLLABUS/CONTENT

- Review of the basic theory of complex analysis

- Rouché's theorem

- Jensen's theorem

- Conformal maps

- Moebius' maps

- Riemann's mapping theorem

- Bloch and Picard theorems

- Theory of functions of finite order and theorems of Weierstrass and Hadamard

- a-points

- Special functions

RECOMMENDED READING/BIBLIOGRAPHY

• Notes on Aulaweb
• Remmert - Classical Topics in Complex Function Theory 
• Stein, Shakarchi - Complex analysis Markushevich - Theory of Functions of a Complex Variable. Volume 2 
• Viola - An introduction to special functions 
• Tao - Online notes

TEACHERS AND EXAM BOARD

Exam Board

SANDRO BETTIN (President)

ALBERTO PERELLI

LESSONS

LESSONS START

In September, at the same time of the other master courses in mathematics

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral exam on the whole program.

Students with a certified DSA, disability or other special educational needs are advised to contact the lecturer at the beginning of the course in order to agree on teaching and examination methods that, while respecting the teaching objectives, take into account individual learning methods and provide suitable compensatory tools.

ASSESSMENT METHODS

During the oral exam the student will have to be able to: state and prove the theorems presented in class, correctly state all the definitions and solve simple exercises. 

Exam schedule