Czech

6

prof. RNDr. Miloslav Druckmüller, CSc.

Institute of Mathematics

Real variable analysis at the basic course level

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.

The aim of the course is to familiarise students with elements of complex analysis and with Fourier transform including applications.  

The course provides students with basic knowledge and skills necessary for using the ecomplex numbers, integrals and residue, usage of  Fourier transforms.

Programme N-MAI-P: Mathematical Engineering, Master's, compulsory

Programme C-AKR-P: , Lifelong learning
specialization CLS: , elective

26 hours, compulsory

1. Complex numbers, Moivre's formula, n-th root
2. Functions of complex variable, limit, continuity, elementary functions
3. Derivative, holomorphic functions, harmonic functions, Cauchy-Riemann equations
4. Harmonic functions, geometric interpretation of derivative in complex domain
5. Series and rows of complex functions, power sets, uniform convergence
6. Curves, integral of complex function, primitive function, integral path independence
7. Cauchy's integral formula, uniqueness theorem
8. Taylor and Laurent series
9. Singular points of holomorphic functions, residue, residue theorem
10. Integration by means of residue theory
11. Conformal mapping
12. Fourier transform
13. Fourier transform aplications