Course detail

Mathematics 2

Ordinary differential equations, basic terms, exact methods, examples of use. Differential calculus in the complex domain, derivative, Caucy-Riemann conditions, holomorphic functions. Integral calculus in the complex domain, Cauchy theorem, Cauchy formula, Laurent series, singular points, residue theorem. Laplace transform, convolution, applications. Fourier transform, relation to the Laplace transform, practical usage. Z transform, discrete systems, difference equations.

Learning outcomes of the course unit

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

Prerequisites

The subject knowledge on the secondary school level and BMA1 course.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Škrášek J., Tichý Z.: Základy aplikované matematiky II. SNTL Praha 1983.
Hlávka J., Klátil J., Kubík S.: Komplexní proměnná v elektrotechnice. SNTL Praha 1990.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Requirements for completion of a course are specified by a regulation issued by the lecturer responsible for the course and updated for every.

Language of instruction

English

Work placements

Not applicable.

Course curriculum

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.

Aims

The student is acquainted with some fundamental methods for solving the ordinary differential equations in the first part and with Laplace, Fourier and Z transforms in the other part.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Classification of course in study plans

• Programme EEKR-BC Bachelor's

branch BC-AMT , 1. year of study, summer semester, 6 credits, compulsory
branch BC-EST , 1. year of study, summer semester, 6 credits, compulsory
branch BC-MET , 1. year of study, summer semester, 6 credits, compulsory
branch BC-SEE , 1. year of study, summer semester, 6 credits, compulsory
branch BC-TLI , 1. year of study, summer semester, 6 credits, compulsory

Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Exercise

12 hours, optionally

Teacher / Lecturer

Computer exercise

14 hours, optionally

Teacher / Lecturer