Course detail

Mathematics - Selected Topics II

FSI-T2KAcad. year: 2014/2015

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 analytic functions, conform mapping, and integration of complex variable functions
including the theory of residua.

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)

Learning outcomes of the course unit

Fundamental knowledge of complex functions analysis.

Prerequisites

Knowledge of mathematical analysis at the basic course level

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

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

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

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

Specification of controlled education, way of implementation and compensation for absences

Missed lessons can be compensated for via a written test.

Recommended optional programme components

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

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B-FIN , 3 year of study, winter semester, compulsory

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 set
10. Isolated singular points of holomorphy functions
11. Residua
12. Using of residua
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 set
10. Isolated singular points of holomorphy functions
11. Integration using residua theory
12. Using of residua
13. Test