Course detail

Mathematics - Selected Topics II

FSI-T2KAcad. year: 2024/2025

The course familiarises students with fundamentals of the complex variable analysis. It gives information about elementary functions of complex variable, about derivative and the theory of holomorphic functions, conform mapping, and integration of complex variable functions including the theory of residue.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

prof. RNDr. Miloslav Druckmüller, CSc.

Department

Institute of Mathematics (ÚM)

Entry knowledge

Knowledge of mathematical analysis at the basic course level

Rules for evaluation and completion of the course

Course-unit credit based on a written test.
Exam has a written and an oral part.


Missed lessons can be compensated via a written test.

Aims

Then aim of the course is to extend students´ knowledge of real variable analysis to complex domain.


Fundamental knowledge of complex functions analysis.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Druckmüller, M., Svoboda, K.: Vybrané statě z matematiky I., skriptum FS VUT Brno, Brno 1986
Druckmüller, M., Ženíšek, A.: Funkce komplexní proměnné, PC-Dir Real, Brno 2000
Šulista, M.: Základy analýzy v komplexním oboru, Stát.nakl.techn.lit., Praha 1981

Recommended reading

Druckmüller, M., Svoboda, K.: Vybrané statě z matematiky I., skriptum FS VUT Brno, Brno 1986
Druckmüller, M., Ženíšek, A.: Funkce komplexní proměnné, PC-Dir Real, Brno 2000 proměnné, PC-Dir Real, Brno 2000
Šulista, M.: Analýza v komplexním oboru, Stát.nakl.techn.lit., Praha 1986
Šulista, M.: Základy analýzy v komplexním oboru, Stát.nakl.techn.lit., Praha 1981

Elearning

eLearning: currently opened course

Classification of course in study plans

  • Programme B-FIN-P Bachelor's 3 year of study, winter semester, compulsory

  • Programme C-AKR-P Lifelong learning

    specialization CZS , 1 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. RNDr. Miloslav Druckmüller, CSc.

Syllabus

1. Complex numbers, Gauss plain, sets of complex numbers
2. Functions of complex variable, limit, continuity, elementary
functions
3. Series and rows of complex numbers
4. Curves
5. Derivative, holomorphy functions, harmonic functions
6. Series and rows of complex functions, power set
7. Integral of complex function
8. Cauchy's theorem, Cauchy's integral formula
9. Laurent series
10. Isolated singular points of holomorphy functions
11. Residue
12. Using of residue
13. Conformal mapping

Exercise

26 hod., compulsory

Teacher / Lecturer

prof. RNDr. Miloslav Druckmüller, CSc.

Syllabus

1. Complex numbers, Gauss plain, sets of complex numbers
2. Functions of complex variable, limit, continuity, elementary
functions
3. Series and rows of complex numbers
4. Curves
5. Derivative, holomorphy functions, harmonic functions
6. Series and rows of complex functions, power set
7. Integral of complex function
8. Cauchy's theorem, Cauchy's integral formula
9. Laurent series
10. Isolated singular points of holomorphy functions
11. Integration using residua theory
12. Using of residue
13. Test

Elearning

eLearning: currently opened course