|
Lecturer(s)
|
|
|
|
Course content
|
1. Complex numbers, modulus, argument. 2. Elementary functions, single-valued branches of multi-valued functions 3. Holomorphic functions 4. Complex integration over curves, Cauchy theorem, Cauchy formula 5. Power series expansion 6. Calculus of residues 7. Fourier series - expansions and pointwise convergence 8. Fourier series in the Hilbert space 9. Fourier transform of functions 10. Fourier transform of distributions 11. Methods of computation of Fourier transforms 12. Classification of PDEs 13. Laplace equation, heat equation, wave equation
|
|
Learning activities and teaching methods
|
|
unspecified
|
|
Learning outcomes
|
The topics include an introduction to complex analysis, Fourier series and integral, and basic information on partial differential equations. These parts of analysis have far reaching applications in science and engineering.
|
|
Prerequisites
|
Teaching in English is meant only for erasmus and foreign students. In the case of a small number of students is teaching in a form of individual consultations.
|
|
Assessment methods and criteria
|
unspecified
|
|
Recommended literature
|
-
KOPÁČEK, J. Matematika pro fyziky III, Matfyzpress, Praha, 1999.
-
KOPÁČEK, J. Matematika pro fyziky IV, Matfyzpress, Praha, 2003.
-
VESELÝ, J. Komplexní analýza, Karolinum, Praha, 2000.
|