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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
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 -

Last update: G_M (16.05.2012)

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

Aim of the course -

Last update: G_M (27.04.2012)

Advanced topics in complex analysis.

Course completion requirements -

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

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.

Literature - Czech

Last update: G_M (27.04.2012)

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

Teaching methods -

Last update: G_M (27.04.2012)

Lecture and exercises

Requirements to the exam -

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

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

Syllabus -

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

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)