Course detail

Mathematics - Selected Topics II

FSI-T2K Acad. year: 2023/2024 Winter semester

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

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.

The study programmes with the given course

Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

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 hours, compulsory

Teacher / Lecturer

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