Course detail

Mathematics - Selected Topics I

FSI-T1KAcad. year: 2007/2008

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

5

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

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

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

Kolmogorov,A.N.,Fomin,S.V.: Základy teorie funkcí a funkcionální analýzy, SNTL Praha 1975 (CS)
Lang, S. Real and Functional Analysis. Third Edition, Springer-Verlag 1993 (EN)

Recommended reading

Kolmogorov,A.N.,Fomin,S.V.: Základy teorie funkcí a funkcionální analýzy, SNTL Praha 1975

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B3940-00 , 2. year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, 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 hours, 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