Lecturer(s)


Vodák Rostislav, RNDr. Ph.D.

Staněk Svatoslav, prof. RNDr. CSc.

Course content

1. Complex numbers and complex functions. 2. Limits and continuity of complex functions. 3. Complex functions of real variables, curves in the complex plane. 4. Differentiation of complex functions, holomorphic functions. 5. Sequences and series of complex functions, power series. 6. Elementary complex functions. 7. Line integrals of complex functions. 8. The Cauchy theorem. Cauchy's formula. Cauchytype integrals. 9. Primitive functions. 10. Taylor series for holomorphic functions. 11. The Laurant series. 12. Singularities of holomorphic functions and their classification. 13. Residue and the residue theorem. 14. Application of residue theorem and the Jordan lemma.

Learning activities and teaching methods

Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
 Attendace
 52 hours per semester
 Preparation for the Course Credit
 20 hours per semester
 Preparation for the Exam
 50 hours per semester

Learning outcomes

Understand the mathematical tools of differential and integral calculus of functions of a complex variable.
Comprehension Understand the mathematical tools of differential and integral calculus of functions of a complex variable.

Prerequisites

Understanding the basic elements of mathematical analysis including the mathematical tools of differential and integral calculus.

Assessment methods and criteria

Oral exam, Written exam
Credit: the student has to pass one written tests (i.e. to obtain at least half of the possible points). Exam: the student has to understand the subject and be able to prove all theorems.

Recommended literature


Černý, I. (1983). Analýza v komplexním oboru. Academia, Praha.

M. A. Jevgrafov a kolektiv. (1976). Sbírka úloh z TFKP. SPN, Praha.
