Course: Complex Variable Analysis

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Course title Complex Variable Analysis
Course code KMA/MFKP8
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 3
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)
  • 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 (Cauchy-Riemann 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.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Teaching Training in Mathematics for Secondary Schools (2015) Pedagogy, teacher training and social care 1 Summer