SubjectsSubjects(version: 845)
Course, academic year 2018/2019
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Complex Analysis 2 - NMMA408
Title in English: Komplexní analýza 2
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2018
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: prof. RNDr. Ondřej Kalenda, Ph.D., DSc.
Class: M Mgr. MA
M Mgr. MA > Povinné
Classification: Mathematics > Real and Complex Analysis
Incompatibility : NMAA015, NMAA067
Interchangeability : 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: prof. RNDr. Ondřej Kalenda, Ph.D., DSc. (25.01.2019)

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.

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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