Course detail

Mathematics 2

FEKT-BPC-MA2Acad. year: 2025/2026

Functions of several variables, partial derivatives, gradient. Ordinary differential equations, basic concepts, examples of the use of differential equations. Differential calculus for a function of a complex variable, derivative of a function, Cauchy-Riemann conditions, holomorphic functions. Integral calculus in the complex domain, Cauchy's theorem, Cauchy's formula, Laurent series, singular points, residue theorem. Laplace transform, concept of convolution, practical applications. Fourier transform, connection with Laplace transform, examples of applications. Z-transform, discrete systems, differentcre equations.

Language of instruction

Czech

Number of ECTS credits

Mode of study

Not applicable.

Guarantor

doc. RNDr. Zdeněk Svoboda, CSc.

Department

Department of Mathematics (UMAT)

Entry knowledge

Knowledge at the level of secondary school study and MA1 is required. To master the subject matter well, it is necessary to be able to determine the definitional domains of common functions of one variable, to understand the concept of limits of a function of one variable, numerical sequences and its limits, and to solve specific standard problems. It is also necessary to know the rules for deriving real functions of one variable, to know the basic methods of integration - integration per partes, the method of substitution for indefinite and definite integrals and to be able to apply these to problems within the scope of the BMA1 scripts. Knowledge of infinite series and some basic criteria for their convergence is also required.

Rules for evaluation and completion of the course

During the semester, students will complete an assessed project consisting of solving individual numerical problems and writing and two teacher-assessed tests. Lectures are not compulsory, exercises are compulsoryry

Aims

Extend knowledge of differential calculus to include methods of functions of several variables, especially calculations and the use of partial derivatives. To introduce students to ordinary differential equations and elementary methods for solving some types of differential equations. To introduce the theory of functions of a complex variable, the methods of which are essential theoretical equipment for students of all electrical engineering disciplines. Finally, to provide students with the ability to solve ordinary problems using the methods of Laplace, Fourier and Z-transforms for linear differential and differential equations.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

KOLÁŘOVÁ, E., Matematika 2, Sbírka úloh, FEKT VUT v Brně 2009 (CS)
ARAMOVIČ, I. G., LUNC, G. L. a El´SGOLC, L. E., Funkcie komplexnej premennej, operátorový počet, teória stability. Alfa Bratislava 1973. (SK)
SVOBODA, Z., VÍTOVEC, J., Matematika 2, FEKT VUT v Brně 2015 (CS)
Zdeněk Svoboda, Jiří Vítovec: Matematika 2, FEKT VUT v Brně

Type of course unit

Lecture

39 hod., optionally

Teacher / Lecturer

doc. RNDr. Zdeněk Svoboda, CSc.

Syllabus

1. Multivariable functions (limit, continuity). Partial derivatives, gradient.
2. Ordinary differential equations of order 1 (separable equation, linear equation, variation of a constant).
3. Homogeneous linear differential equation of order n with constant coefficients.
4. Non homogeneous linear differential equation of order n with constant coefficients.
5. Functionss in the complex domain.
6. Derivative of a function. Caychy-Riemann conditions, holomorphic funkction.
7. Integral calculus in the complex domain, the Cauchy theorem, the Cauchy formula.
8. Laurent series, singular points and their classification.
9. Residue, Residual theorem
10. Fourier series, Fourier transforms.
11. Direct Laplace transform, convolution, grammar of the transform.
12. Inverse Laplace transform, aplications.
13. Direct and inverse Z transforms. Discrete systems, difference eqautions.

Fundamentals seminar

8 hod., compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Svoboda, CSc.

Syllabus

Computer-assisted exercise

18 hod., compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Svoboda, CSc.

Syllabus

Individual topics in accordance with the lecture.

VUT

Faculties

University Institutes

Parts

Mathematics 2

Type of course unit