Course detail

Calculus of the more variable functions, ordinary differential equations, basic terms, exact methods, examples of differential equation use, complex functions basic terms, differential and integral calculus, Cauchy theorem, Laurent series, residue theorem. Fourier series and Fourier transform, Laplace transform, and its practical usage. Z transform and application of its to difference equations . Basic of numerical mathematics and methods,. Basic of probability, random variable, law of large numbers. Basic of mathematical statistics.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Learning outcomes of the course unit

After the completion of the course the students should be able
- use some methods to solve differential equations
- use Laplace and Fourier transformation for solving differential and integral equations in physics and engineering
- use Z- transformation for solving discrete equations
- define the basic principles of numerical analysis
- use the methods of probability and statistics in concrete problems

Prerequisites

The subject knowledge on the high school level course is requested. Explain the basic principles and methods of higher mathematics on the course BMA1 level.

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

upto 30 points from computer exercises and the other activities
upto 70 points from examination paper

Course curriculum

1. Calculus of the more variable functions.
2. Ordinary differential equations, basic terms, exact methods for the equation of the 1. order
3. Linear difeferential equations.
4. Complex functions - basic terms and differential calculus.
5. Basic of integral calculus Cauchy theorem.
6. Laurent series, residue theorem.
7. Fourier series and Fourier transform.
8. Laplace transform, and its usage.
9. Z transform and application of its to difference equations .
10. Basic of numerical mathematics and methods,.
11. Basic of probability.
12. Random variable.
13. Law of large numbers and basic of mathematical statistics.

Work placements

Not applicable.

Aims

The students are acquainted with some fundamental methods for solving the ordinary differential equations and as application of the knowledge of complex analysis with Laplace, Fourier and Z transforms in the first part. Other parts are devoted to introduction into numerical methods and probability.

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

Not applicable.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Kolářová, E.:MATEMATIKA 2 Sbírka úloh (CS)
Chvalina, J., Svoboda, Z., Novák,M.: Matematika 2 (CS)
Melkes, F., Řezáč, M.: Matematika 2(BMA2 et KMA2) (CS)
FAJMON, B., RŮŽIČKOVÁ, I. MATEMATIKA_3_S.PDF. Matematika 3. Brno: UMAT FEKT VUT, 2003. s. 1-266. (CS)
Hlavičková, I., Hliněná, D.: Matematika 3 - sbírka úloh z pravděpodobnosti (CS)

Not applicable.

Classification of course in study plans

• Programme ZRZT-J Bachelor's

branch J-ZRT , 1. year of study, summer semester, compulsory

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Exercise in computer lab

26 hours, optionally

Teacher / Lecturer

The other activities

13 hours, optionally

Teacher / Lecturer