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Mandatory course for the master study branch Mathematical analysis. Recommended for the first year of master
studies. Introduction to advanced topics in complex analysis - harmonic functions of two real variables and their
relationship to holomorphic functions, boundary behaviour of holomorphic functions, analytic continuation,
elements of the theory of functions of several complex variables.
Last update: T_KMA (02.05.2013)
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The credit (zápočet) is a necessary condition for coming to examination.
Students obtain the credit for giving short lectures on given topics during classes. The character of the credit does not enable its repetition. Last update: Kalenda Ondřej, prof. RNDr., Ph.D., DSc. (25.01.2019)
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Rudin, W.: Real and complex analysis, McGraw-Hill, New York, 1966.
Taylor, J. L.: Several complex variables with connections to algebraic geometry and Lie groups, AMS, Providence, Rhode Island, 2005.
Last update: T_KMA (02.05.2013)
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Rules for 2018/2019:
A necessary condition for passing the exam is to gain the credit in advance.
The exam will have the oral form. Each student will draw a set of questions. The individual question will consits of the proofs of theorems presented during the lectures and of problems which can be solved using the methods explained during the course. The necessary and sufficient condition to pass the exam is to gain at least 50% points. Last update: Lávička Roman, doc. RNDr., Ph.D. (18.02.2020)
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1. Harmonic funcrtions of two variables (relationship of harmonic and holomorphic functions, Poisson integral, Schwarz relfection principle, boundary behaviour of harmonic and holomorphic functions, Hardy spaces on the disc)
2. Analytic functions (basic properties, monodromy theorem, Riemannian manifolds, singularities of analytic functions).
3. Functions of several complex variables (domains of convergence of power series, Hartogs' paradox and Hartogs' theorem). Last update: T_KMA (02.05.2013)
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Knowledge of complex analysis in the extent of the courses
Introduction to Complex Analysis - NMMA301
Complex Analysis 1 - NMMA338 Last update: Lávička Roman, doc. RNDr., Ph.D. (21.05.2018)
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