Functions of Complex Variable

Course guarantor:

Pavel Šťovíček

Lecturer:

Severin Pošta, Pavel Šťovíček

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course develops advanced properties of systems of holomorphic functions, Ascoli-Vitali's theorem, advanced properties of conformal mappings, transcendental and meromorphic functions. Basic properties of complex functions of several complex variables together with improper line integrals and its applications are presented.

Requirements:

Mathematical analysis courses (01MA1, 01MAA2-4 or 01MAB2-4)

Syllabus of lectures:

1. Review of basic theorems of complex analysis. 2. Fundamental properties of the holomorphic functions, normal family of holomorfic functions in connected region, Ascoli-Vitali's theorem. 3. Theorem of Riemann, conformal mapping. 4. Transcendental and meromorphic functions. 5. Generalized series in C. 6. Complex functions of several complex variables. 7. Holomorphic functions of several complex variables. 8. Improper line integrals with parameters. 9. Holomorphic functions and line integrals with parameters. 10. Bessel functions and line integrals with parameters.

Syllabus of tutorials:

No lecture exercises.

Study Objective:

Active knowledge of properties of holomorphic function systems and basic properties of functions of several complex variable.

Study materials:

[1] I. Černý: Foundations of Analysis in the Complex Domain. Academia, Praha 1992

[2] W. Rudin: Real and complex analysis, McGraw-Hill, Boston 1987

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: