Course detail

Mathematics 2

FEKT-BPC-MA2Acad. year: 2026/2027

Functions of several variables, partial derivatives, gradient. Ordinary differential equations, basic concepts, examples of the application of differential equations. Differential calculus for functions of a complex variable, differentiation of functions, Cauchy–Riemann conditions, holomorphic functions. Integral calculus in the complex plane, Cauchy’s theorem, Cauchy’s formula, Laurent series, singular points, residue theorem. Laplace transform, the concept of convolution, practical applications. Fourier transform, connection to the Laplace transform, examples of use. Z-transform, discrete systems, difference equations.

 

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. RNDr. Zdeněk Svoboda, CSc.

Department

Department of Mathematics (UMAT)

Entry knowledge

Knowledge equivalent to that acquired in high school and in the MA1 course is required. To master the course material, students must be able to determine the domains of common functions of one variable, understand the concept of limits of functions of one variable and numerical sequences and their limits, and solve specific standard problems. Furthermore, students must know the rules for differentiating real functions of one variable, be familiar with basic integration methods—integration by parts and the substitution method for both indefinite and definite integrals—and be able to apply these methods to problems covered in the MA1 course materials. Knowledge of infinite numerical series and some basic convergence criteria is also required.

Rules for evaluation and completion of the course

During the semester, students will take two tests graded by the instructor (each worth a maximum of 2 × 15 points).  The course concludes with a written exam worth a maximum of 70 points. A minimum of 10 points is required to earn credit.
Lectures are not mandatory; seminars are mandatory. 

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

Recommended reading

MELKES, F., ŘEZÁČ, M., Matematika 2, FEKT VUT v Brně 2002 (CS)

Classification of course in study plans

  • Programme BPC-TLI Bachelor's 1 year of study, summer semester, compulsory, fundamental theoretical courses of the profile core
  • Programme BPC-SEE Bachelor's 1 year of study, summer semester, compulsory, fundamental theoretical courses of the profile core
  • Programme BPC-NCP Bachelor's 1 year of study, summer semester, compulsory
  • Programme BPC-MET Bachelor's 1 year of study, summer semester, compulsory, fundamental theoretical courses of the profile core
  • Programme BPC-IBE Bachelor's 1 year of study, summer semester, compulsory, fundamental theoretical courses of the profile core
  • Programme BPC-EMU Bachelor's 1 year of study, summer semester, compulsory
  • Programme BPC-ECT Bachelor's 1 year of study, summer semester, compulsory, fundamental theoretical courses of the profile core
  • Programme BPC-BTB Bachelor's 1 year of study, summer semester, compulsory

  • Programme BPC-AUD Bachelor's

    specialization AUDB-ZVUK , 1 year of study, summer semester, compulsory, fundamental theoretical courses of the profile core
    specialization AUDB-TECH , 1 year of study, summer semester, compulsory, fundamental theoretical courses of the profile core

  • Programme BPC-AMT Bachelor's 1 year of study, summer semester, compulsory, fundamental theoretical courses of the profile core
  • Programme BIT Bachelor's 2 year of study, summer semester, elective
  • Programme BIT Bachelor's 2 year of study, summer semester, elective

Type of course unit

 

Lecture

39 hours, 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 hours, compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Svoboda, CSc.

Syllabus

 

Computer-assisted exercise

18 hours, compulsory

Teacher / Lecturer

doc. RNDr. Zdeněk Svoboda, CSc.

Syllabus

Individual topics in accordance with the lecture.