Course: Complex Variable Analysis 1

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Course title Complex Variable Analysis 1
Course code KMA/FKP1M
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Vodák Rostislav, RNDr. Ph.D.
  • Pastor Karel, doc. Mgr. Ph.D.
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. Cauchy-type 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
Knowledge of differential and integral calculus of two variables.

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.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Mathematics and Applications (1) Mathematics courses 3 Winter