Czech

6

Not applicable.

The acquired mathematical knowledge and practical computational skills are especially an important starting point for acquiring new knowledge in computer science and economically oriented fields, supporting the correct use of mathematical software, and for further expanding knowledge and skills in math mathematical subjects.

Mathematics 1 and 2.

Not applicable.

Teaching is divided into lectures and exercises. The lectures focus on explaining the theory with reference to applications, exercises on practical calculations and application tasks.

Requirements for credit:
- Active participation in the seminar, attendance at the seminar is compulsory,
- fulfillment of individual tasks and written assignments,
-Solving control tests and gaining more than 50% points.

The examination has a written and an oral part, with the written part of the exam.
The written part lasts 2 hours.
If the student fails to reach at least 50% of the total number of points achieved, the written part and the whole examination are assessed as "F" (unsatisfactory) and the student does not go to the oral part.
The oral part follows a written one, the duration of which does not normally exceed 10 minutes. Its main purpose is to clarify the classification. During the oral part the student has the opportunity to get acquainted with the specific evaluation of individual tasks. The oral exam also serves to resolve any uncertainties in the written part. If there are reasons for the examiner, student, additional questions may be asked. Students have the right to request preparation time for their preparation.

1. Endless series of numbers (sum, necessary and sufficient conditions of convergence, properties, absolute and relatively convergent series)
2. Power series (sum, radius of convergence, properties)
3. Application of power series (approximate calculations of function values, integral and differential equations)
4. Fourier series (sum, properties, applications)
5. Rational lesion function in the complex field (complex roots and singularity, decomposition on partial fragments)
6. Laplace transform (definition, properties, inverse Laplace transform)
7. Use of L-transformation to solve ODR
8. Differential equations
9. Z-transformation (definition, properties, inverse Z-transformation, use to solve differential equations)
10. Fourier transform (definitions, properties, applications)
11. Mathematical optimization (convex sets and functions, mathematical programming tasks)
12. Linear programming (the role of LP and its properties, the basics of the simplex method, duality, Farkas theorem)

Not applicable.

The aim is to build up the mathematical apparatus necessary for the interpretation of follow-up professional subjects and to master the considerations and calculations in the field of the given subject matter (including with regard to the use of computer technology) including applications in computer science and economic disciplines.

Attendance at lectures is not checked. Participation in the exercises is mandatory and is systematically checked. The student is obliged to apologize for abstention and it is entirely up to the teacher to judge the reason for the excuse. Forms of replacement for missed lessons are determined by the teacher individually.

Not applicable.

Not applicable.

DOŠLÁ Z., PLCH R. a SOJKA P.: Nekonečné řady, MU v Brně, 2002, ISBN 80-210-3005-4
KROPÁČ J., KUBEN J.: Fukce gama a beta, transformace Laplaceova, Z a Fourierova, 3.vydání, VA v Brně, 2002 (CS)
DUPAČOVÁ, J., LACHOUT, P . Úvod do optimalizace. Vyd. 1. Praha: Matfyzpress, 2011, 81 s. ISBN 978-80-7378-176-7.

JURA, P.: Signály a systémy. Elektronické skriptum, část I, II, III, druhé opravené vydání, 2010 (CS)
JACQUES, I.: Mathematics for economics and business. Second edition. Addison-Wesley, Wokingham 1994, 485s, ISBN 0-201-42769-9
WISNIEWSKI, M.: Introductory mathematical methods in economics. First edition. McGraw-Hill, London 1991, 257s, ISBN 0-07-707407-6

26 hours, compulsory

Teaching is divided into lectures and exercises. The lectures focus on explaining the theory with reference to applications, exercises on practical calculations and application tasks.