Code: 01FKP 
Functions of Complex Variable 
Lecturer: 
Weekly load: 2+0 
Completion: EX 
Department: 14101 
Credits: 2 
Semester: W 
 Description:

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.
 Contents:

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.
 Seminar contents:

No lecture exercises.
 Recommended literature:

[1] I. Černý: Foundations of Analysis in the Complex Domain. Academia, Praha 1992
[2] W. Rudin: Real and complex analysis, McGrawHill, Boston 1987
 Keywords:
 complex variable, several complex variables, holomorphic functions, conformal mapping, Bessel functions, line integrals
Abbreviations used:
Semester:
 W ... winter semester (usually October  February)
 S ... spring semester (usually March  June)
 W,S ... both semesters
Mode of completion of the course:
 A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
 GA ... Graded Assessment (a grade is awarded for this course)
 EX ... Examination (a grade is awarded for this course)
 A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)
Weekly load (hours per week):
 P ... lecture
 C ... seminar
 L ... laboratory
 R ... proseminar
 S ... seminar