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Lecturer(s)
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Tomeček Jan, doc. RNDr. Ph.D.
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Vodák Rostislav, RNDr. Ph.D.
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Course content
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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.
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Learning activities and teaching methods
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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
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Learning outcomes
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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.
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Prerequisites
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Knowledge of differential and integral calculus of functions of real variables.
KMA/ZMA1
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Assessment methods and criteria
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Oral exam, Written exam
Credit: active participation, homework. Exam: written test, the student has to understand the subject and prove principal results.
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Recommended literature
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J. B. Conway. (1984). Functions of One Complex Variable. Springer New York Inc.
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J. Zeman. (1998). Úvod do komplexní analýzy. Vydavatelství UP Olomouc.
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