Course detail
Mathematics 2
FEKT-BPC-MA2Acad. year: 2024/2025
561 / 5000
Výsledky překladu
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
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Lectures are not mandatory, exercises are mandatory
Aims
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
Prerequisites and corequisites
Basic literature
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
Elearning
Classification of course in study plans
- Programme BPC-AMT Bachelor's 1 year of study, summer semester, compulsory
- Programme BPC-AUD Bachelor's
specialization AUDB-TECH , 1 year of study, summer semester, compulsory
specialization AUDB-ZVUK , 1 year of study, summer semester, compulsory - Programme BPC-ECT 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
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus
Computer-assisted exercise
Teacher / Lecturer
Syllabus
Project
Teacher / Lecturer
Syllabus
Elearning