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Complex Analysis 2 - NMMA408

Title:	Komplexní analýza 2
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2016
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. Mgr. Petr Honzík, Ph.D.
Class:	M Mgr. MA M Mgr. MA > Povinné
Classification:	Mathematics > Real and Complex Analysis
Incompatibility :	NMAA015, NMAA067
Interchangeability :	NMAA067
Is interchangeable with:	NMAA067

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Annotation -

Last update: T_KMA (02.05.2013)

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.

Literature -

Last update: T_KMA (02.05.2013)

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.

Syllabus -

Last update: T_KMA (02.05.2013)

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).