The course introduces advanced topics in complex analysis.
Advanced notions of functions of a complex variable, including: Gamma function, Rouche and Picard theorems, Riemann map theorem and main properties of order finished.
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.
The main prerequisite is the basic theory of complex analysis.
52 hours of frontal lectures.
- 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
Ricevimento: By appointment
SANDRO BETTIN (President)
ALBERTO PERELLI
In September, at the same time of the other master courses in mathematics
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.
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.
