Functions of Complex Variable and Integral Transformations

Here you can find some basic information about the subject. Pay attention to remarks below, you might find them useful.

• Description
• Credit
• Projects
• Seminary
• Materials

Description

Functions of complex variable and integral transformations are one of the basic tools of effective solution of technical problems. The students will get knowledge of basic concepts of functions of complex variable and integral transformations.

Credit

You can achieve up to 30 points:

• 1. test (complex numbers and their sets, complex functions and their derivatives) - 7b (Sample test (czech))
• 2. test (conformal mappings, integrals of complex functions Power and Taylor series) - 7b (Sample test (czech))
• 1. project (Fourier series) - 8b
• 2. project (Laplace transform) - 8b

To gain credit you need to achieve at least 15pts.

Exam:

Projects

You can write your projects either by hand or in electronic form. The projects can be handed over anytime during the semester, however the sooner the better.

Seminary

Brief summary of subject matter (PDF, czech)

Elementary derivatives and antiderivatives

Table values of sine and cosine (Thanks to Ing. Martin Mrovec, Ph.D. PDF here):

Seminary programme

1. Complex numbers, basic operations, Gauss plane

2. Sets and their visualising in Gauss plane

3. Elementary complex functions, real and imaginary part of the function

4. Derivative of complex function, Cauchy-Riemann conditions

5. Conformal mappings, linear rational functions

6. FIRST TEST, integrals of complex function

7. Cauchy's theorem, Cauchy's integral formulae, path-independence of integral

8. Fourier series - calculation of coefficients, spectrum, project info

9. Fourier series - finishing, Power series

10. Taylor series

11. SECOND TEST

12. Laurent series, classification of singularities

13. Residues, residue theorem, subject summary

14. Spare seminary, exam consultations