SubjectsSubjects(version: 944)
Course, academic year 2023/2024
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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 2023
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, English
Teaching methods: full-time
Teaching methods: full-time
Class: M Mgr. MA
M Mgr. MA > Povinné
Classification: Mathematics > Real and Complex Analysis
Incompatibility : NMAA015, NMAA067
Interchangeability : NMAA067
Is interchangeable with: NMAA067
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.
Course completion requirements -
Last update: prof. RNDr. Ondřej Kalenda, Ph.D., DSc. (25.01.2019)

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 -
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.

Requirements to the exam -
Last update: doc. RNDr. Roman Lávička, Ph.D. (18.02.2020)

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

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).

Entry requirements -
Last update: doc. RNDr. Roman Lávička, Ph.D. (21.05.2018)

Knowledge of complex analysis in the extent of the courses

Introduction to Complex Analysis - NMMA301

Complex Analysis 1 - NMMA338

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