Czech

Not applicable.

The absolvent of the subject is able:

- to compute the partial derivatives of the functions of more variables and use the formulas for the gradient and the tangential plane;
- to distinguish between the separable and linear differential equations and also to solve them;
- to solve linear differential equations of higher order with a special right hand side;
- to figure out from the Cauchy Riemann conditions, if the complex function is holomorfic or not, and to derive the holomorfic funcions;
- to compute, using the definition, the integral from the complex function through a curve, to apply the Cauchy theorem for the integral of the holomorfic funcion;
- to establish the poles and to calculate a residue at asimple and at a pole of higher order, to apply the residue theorem for the integral of the meromorfic funcion;
- to solve differential equations by the Laplace transform;
- to find the real Fourier series of an odd, even and a general function, expand a function to sine or cosine series;
- to solve difference equations by the Z- transform.

The subject knowledge on the secondary school level and BMA1 course. For having a facility for subject matter is needed to can determined domains of usual functions of one real variable, to understanding of a concept ot the limit of functions of one real variable and a concept numerical sequences and their limits and to solve conrete standard tasks. Further there is needed the knowledge of rules for derivations of real functions of one variable, the knowledge of basic methods of integrations - the integration per partes, by the method of substitution at the indefinit and definit integral have a facilitu for applications on tasks with respect to extent of the teaching text BMA1. Knowledges of infinite numerical series and some basic criteria of their convergence is also required.

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. They consists into lectures according the contents of a subject matter and in the solving of examples, as well as in the practising of other examples containing in the teaching materials of the topic.

Maximum 20 points for individual assignments during the semester (at least 5 points for the course-unit credit); maximum 80 points for a written exam.

1. Calculus of the more variable functions.
2. Ordinary differential equations, basic terms.
3. Solutions of linear differential equations of first order.
4. Homogenius linear differential equations of higher order.
5. Solutions of nonhomogenious linear differential equations with constant coefficients.
6. Differential calculus in the complex domain, derivative.
7. Caucy-Riemann conditions, holomorphic functions.
8. Integral calculus in the complex domain, Cauchy theorem, Cauchy formula.
9. Laurent series, singular points.
10. Residue theorem.
11. Laplace transform, convolution, Heaviside theorems, applications.
12. Fourier transform, relation to the Laplace transform, practical usage.
13. Z transform, discrete systems, difference equations.

Not applicable.

To extent the student knowlidges on methods of functions of several variables and onto application of partial derivatives. Further, in the other part, to aquiant students with some elementary methods for solving the ordinary differential equations and to make possible a deeper inside into the theory of functions of a complex vairiable, the methods of which are a necessary theoretical equipment of a student of all electrotechnical disciplines. Finally, to provide students by abillity to solve usual tasks by methods of Laplace, Fourier and Z transforms.

Tutorials are not compulsory.

Not applicable.

Not applicable.

KOLÁŘOVÁ, E., Matematika 2, Sbírka úloh, FEKT VUT v Brně 2009 (CS)
SVOBODA, Z., VÍTOVEC, J., Matematika 2, FEKT VUT v Brně 2015 (CS)

Not applicable.