Lecturer(s)


Staněk Svatoslav, prof. RNDr. CSc.

Course content

1. Complex plane, extended Gauss plane. 2. Functions of a complex variable (limit, continuity). 3. Derivative of functions of a complex variable (CauchyRiemann conditions). 4. Holomorphic functions. 5. Conformal mapping. 6. Elementary functions of a complex variable. 7. Sequences and series of functions, power series. 8. Plane curves. 9. Integrals of functions of a complex variable. 10. Cauchy theorem, Cauchy integral formula. 11. Primitive functions. 12. Taylor series. 13. Zero points of holomorphic functions. 14. Isolated singularities. 15. Laurent series. 16. Residue, residue theorem and its application.

Learning activities and teaching methods

Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
 Homework for Teaching
 20 hours per semester
 Attendace
 39 hours per semester
 Preparation for the Exam
 30 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

Knowledge of differential and integral calculus of functions of real variables.

Assessment methods and criteria

Oral exam, Written exam
Credit: active participation, homework. Exam: written test, the student has to understand the subject and prove principal results.

Recommended literature


J. B. Conway. (1984). Functions of One Complex Variable. Springer New York Inc.

J. Zeman. (1998). Úvod do komplexní analýzy. Vydavatelství UP Olomouc.
