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Complex Analysis 1 - NMMA338

Title:	Komplexní analýza 1
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
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:	not taught
Language:	Czech
Teaching methods:	full-time

Class:	M Bc. OM M Bc. OM > Zaměření MA M Bc. OM > Povinně volitelné
Classification:	Mathematics > Real and Complex Analysis
Co-requisite :	NMMA301
Incompatibility :	NMAA016
Interchangeability :	NMAA016, NMMA410
Is pre-requisite for:	NMMA349
Is interchangeable with:	NMMA410, NMAA016

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Annotation -

Advanced Complex Analysis for bachelor's program in General Mathematics. Recommended for specializations Mathematical Analysis.

Last update: G_M (16.05.2012)

Aim of the course -

Advanced topics in complex analysis.

Last update: G_M (27.04.2012)

Course completion requirements -

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: Lávička Roman, doc. RNDr., Ph.D. (24.02.2021)

Literature - Czech

Rudin, W.: Reálná a komplexní analýza, Academia Praha, 1977

Novák, B.: Funkce komplexní proměnné (skripta), SPN Praha, 1980

Luecking, D.H., Rubel, L.A.: Complex Analysis, A Functional Analysis Approach, Springer-Verlag, Universitext, 1984

Veselý, J.: Komplexní analýza, Karolinum Praha, 2000

Last update: G_M (27.04.2012)

Teaching methods -

Lecture and exercises

Last update: G_M (27.04.2012)

Requirements to the exam -

Requirements to the exam correspond to the syllabus to the extent to which topics were covered during the course.

Last update: Lávička Roman, doc. RNDr., Ph.D. (24.02.2021)

Syllabus -

Entire and meromorphic functions (infinite products, the Weierstrass product theorem, the Mittag-Leffler theorem, Cauchy's method)

Properties of the space H(G) of holomorphic functions on an open set G.

Characterization of the dual H(G)*, applications of the Hahn-Banach theorem: Runge's theorems.

Conformal mappings (homographic transformations, the Schwarz lemma, Blaschke's factors, the Riemann theorem)

Last update: Kaplický Petr, doc. Mgr., Ph.D. (29.05.2017)