Course detail

Mathematics 3

FP-MA3_MAcad. year: 2020/2021

It is part of the theoretical basis of the field and follows the subjects Mathematics 1 and 2. It is the basis of theory and application of endless series, differential equations, selected integral transformations and the basics of mathematical optimization.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Learning outcomes of the course unit

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.

Prerequisites

Mathematics 1 and 2.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

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.

Assesment methods and criteria linked to learning outcomes

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.

Course curriculum

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)

Work placements

Not applicable.

Aims

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.

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

Attendance at lectures and exercises (seminars) is not checked.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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.

Recommended reading

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

eLearning

Classification of course in study plans

  • Programme BAK-MIn-D Bachelor's

    branch BAK-MIn , 2. year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

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.

Exercise

26 hours, optionally

Teacher / Lecturer

Syllabus

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.

eLearning