Course detail

Mathematics 2

561 / 5000
Functions of several variables, partial derivatives, gradient. Ordinary differential equations, basic concepts, examples of using differential equations. Differential calculus in the complex field, derivation of a function, Cauchy-Riemann conditions, holomorphic functions. Integral calculus in a complex field, Cauchy's theorem, Cauchy's formula, Laurent series, singular points, residual theorem. Laplace transform, concept of convolution, practical applications. Fourier transform, connection with 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.

Entry knowledge

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.

Rules for evaluation and completion of the course

During of the semester students elaborate two evaluated projects consisting in the solving of individual numeric tasks and they will be writing two tests evaluated by the teacher.
Lectures are not mandatory, exercises are mandatory

Aims

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

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

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

eLearning

Classification of course in study plans

• Programme BPC-AUD Bachelor's

specialization AUDB-ZVUK , 1. year of study, summer semester, compulsory
specialization AUDB-TECH , 1. year of study, summer semester, compulsory

• Programme BPC-AMT Bachelor's, 1. year of study, summer semester, compulsory
• Programme BPC-EKT Bachelor's, 1. year of study, summer semester, compulsory
• Programme BPC-IBE Bachelor's, 1. year of study, summer semester, compulsory
• Programme BPC-MET Bachelor's, 1. year of study, summer semester, compulsory
• Programme BPC-SEE Bachelor's, 1. year of study, summer semester, compulsory
• Programme BPC-TLI Bachelor's, 1. year of study, summer semester, compulsory

Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

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

6 hours, compulsory

Teacher / Lecturer

Syllabus

Individual topics in accordance with the lecture.

Computer-assisted exercise

14 hours, compulsory

Teacher / Lecturer

Syllabus

Individual topics in accordance with the lecture.

Project

6 hours, compulsory

Teacher / Lecturer

Syllabus

Individual topics in accordance with the lecture.

eLearning