Czech

6

Not applicable.

Students will be acquainted with some exact and numerical methods for differential equation solving and with the grounding of technique for formalized solution using Laplace, Fourier and Z transforms.

The subject knowledge on the secondary school level and AMA1 course.

Not applicable.

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

Requirements for completion of a course are specified by a regulation issued by the lecturer responsible for the course and updated for every.

1. Fuctions of several variables, mappings (limit, continuity). Partial derivatives, gradient.
2. Ordinary differential equations and systems of differential equations. Basic concepts and foundations of qualitative theory (existence and uniqueness of solutions of ODE´s, stability). Linear differential equations of the n-th order with constant coefficients, stability of solutions.
3. Difference equations. Basic concepts and foundations of qualitative theory (existence and uniqueness of solutions of DE´s). Linear difference equations.
4. Functions of a complex variable, derivative of complex functions. Integral calculus in complex domain, Cauchy theorem, Cauchy formula.
5.Laurent series, singular points and their classification, residuum and residua-theorem.
6. Mathematical methods for description of signals. Distribution, harmonic functions, periodical functions and Fourier series.
7. Direct and inverse Fourier transformation. Grammar of transform. Applications.
8.Direct and inverse Laplace transformation. Connection with the Fourier transform. Grammar of transform.
9. Applications of the Laplace transform to solving of differential equations and their systems.
10. Direct and inverse Z-transformation. Using the Z-trasformations for solving of difference equations.
11. Signals and their classifications. Continuous-time signals, periodical and harmonic signal, aperiodical signals, spectra of signals.
12. Sytems - concept and cassification. Mathematical model of a continuous-time system and solving of the input-output equation by Laplace transform.Impulse and frequency characteristic.
13. Connections between systems - serial, parallel connection of systems, feedback. Stability of systems.

Not applicable.

The student is acquainted with some fundamental methods for solving the ordinary differential equations in the first part and with Laplace, Fourier and Z transforms in the other part.

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Not applicable.

Not applicable.

Hlávka J., Klátil J., Kubík S.: Komplexní proměnná v elektrotechnice. SNTL Praha 1990.
Škrášek J., Tichý Z.: Základy aplikované matematiky II. SNTL Praha 1983.
Aramanovič, I.G., Lunc, G. L., Elsgolc, L.E.: Funkcie komplexnej premennej, Operátorový počet, Teória stability
Chvalina, J., Svoboda, Z., Novák,M.: Matematika 2
Melkes, F., Řezáč, M.: Matematika 2(BMA2 et KMA2)
Kolářová, E.:MATEMATIKA 2 Sbírka úloh Sbírka úloh RNDr. Edita Kolářová

Not applicable.

13 hours, compulsory

Individual topics in accordance with the lecture.