Functions of Complex Variable B
Code  Completion  Credits  Range  Language 

01FKPB  Z  2  2+0  Czech 
 Course guarantor:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The course develops advanced properties of systems of holomorphic functions, AscoliVitali'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, 01MAA24 or 01MAB24)
 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, AscoliVitali'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, McGrawHill, Boston 1987
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: