Course detail

Mathematics 2

FEKT-CMA2Acad. year: 2011/2012

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.

Language of instruction

English

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

prof. RNDr. Jan Chvalina, DrSc.

Department

Department of Mathematics (UMAT)

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.

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.

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.

Work placements

Not applicable.

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EECC Bc. Bachelor's

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

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

prof. RNDr. Jan Chvalina, DrSc.

Syllabus

1. Ordinary differential equations of order 1 (separable equation, linear equation, variation of a constant).
2. Linear differential equation of order n with constant coefficients.
3. Function of complex variable - transform of a complex plane.
4. Differential calculus in the complex domain, Caychy-Riemann conditions, holomorphic funkction.
5. Basic transcendental functions, application to the electrostatic field.
6. Integral calculus in the complex domain, the Cauchy theorem, the Cauchy formula.
7. Laurent series, singular points and their classification, residues and residue theorem.
8. Direct Laplace transform, convolution, grammar of the transform.
9. Inverse Laplace transform, pulses, electric circuits.
10. Fourier series (trigonometric and exponential forms, basic properties).
11. Direct and inverse Fourier transforms, relation to the Laplace transform, the pulse nad spectrum widths.
12. Direct and inverse Z transforms.
13. Difference eqautions solved using Z transform.

Fundamentals seminar

12 hod., optionally

Teacher / Lecturer

prof. RNDr. Jan Chvalina, DrSc.

Syllabus

Individual topics in accordance with the lecture.

Exercise in computer lab

14 hod., optionally

Teacher / Lecturer

prof. RNDr. Jan Chvalina, DrSc.

Syllabus

Individual topics in accordance with the lecture.