Course detail

Mathematics

FAST-AA01Acad. year: 2024/2025

Basics of linear algebra (matrices, determinants, systems of linear algebraic equations). Some notions of vector algebra and their use in analytic geometry. Function of one variable, limit, continuous functionst, derivative of a function. Some elementary functions, Taylor polynomial. Basics of calculus. Probability. Random varibles, laws of distribution, numeric charakteristics. Sampling, processing statistical data.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

RNDr. Radko Odehnal

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

Basics of mathematics as taugth at secondary schools. Graphs of elementary functions (powers and roots, quadratic function, direct and indirect proportion, absolute value, trigonometric functions) and basic properties of such functions. Simplification of algebraic expression, geometric vector and basics of analytic geometry in E3.

Rules for evaluation and completion of the course

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Aims

The students should learn about the basics of linear algebra, solutions to systems of linear algebraic equations, calculus, theory of probability and statistics.
Students will have a short overview on methods of higher mathematics(operations with matrices, algebra of vectors, differential and integral calculus of functions of one variable, differential calculus of functions of several variables, probability and statistics).

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Larson R., Hostetler R.P., Edwards B.H.: Calculus (with analytic geometry). Brooks Cole, 2005. (EN)
Novotný, J.: Základy lineární algebry. FAST - studijní opora v intranetu, 2005. (CS)
Dlouhý, O., Tryhuk, V.: Reálná funkce dvou a více proměnných. FAST - studijní opora v intranetu, 2005. (CS)
Daněček, J., Dlouhý, O., Přibyl, O.: Neurčitý integrál. FAST - studijní opora v intranetu, 2007. (CS)
Daněček, J., Dlouhý, O., Přibyl, O.: Určitý integrál. FAST - studijní opora v intranetu, 2007. (CS)
Tryhuk, V., Dlouhý, O.: Vektorový počet a jeho aplikace. FAST - studijní opora v intranetu, 2007. (CS)
Dlouhý, O., Tryhuk, V.: Reálná funkce jedné reálné proměnné. FAST - studijní opora v intranetu, 2008. (CS)
KOUTKOVÁ, Helena, Mill, Ivo: Základy pravděpodobnosti, Akademické nakladatelství CERM, s.r.o., Brno 2008. ISBN: 978-80-7204-574-7 (CS) (CS)

Recommended literature

Daněček: Sbírka příkladů z matematiky I. CERM Brno, 2006. (CS)
Koutková, H., Moll, I.: Základy pravděpodobnosti. CERM, 2008. (CS)
Koutková, H., Dlouhý, O.: Sbírka příkladů z pravděpodobnosti a matematické statistiky. CERM Brno, 2008. (CS)

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

RNDr. Radko Odehnal

Syllabus

1. Matrices, basic operations. 2. Systems of linear algebraic equations, Gauss elimination method. 3. Basics of vector algebra, dot, cross, and scalar triple product. 4. Functions of one variable. Limit, continuity and derivative of a function. 5. Some elementary functions, their properties, approximation by Taylor polynomial. 6. Antiderivative and indefinite integral, Newton integral. 7. Riemann’s integral and its calculation, some applications in geometry and physics. 8. Numeric calculation of a definite integral. 9. Two- and more-functions, partial derivative and its use. 10. Probability, random variables. 11. Numerical characteritics of a random variable. 12. Basic distributions. 13. Random sampling, statistics

Exercise

13 hod., compulsory

Teacher / Lecturer

RNDr. Radko Odehnal

Syllabus

1. Matrices, basic operations. 2. Systems of linear algebraic equations, Gauss elimination method. 3. Basics of vector algebra, dot, cross, and scalar triple product. 4. Functions of one variable. Limit, continuity and derivative of a function. 5. Some elementary functions, their properties, approximation by Taylor polynomial. 6. Antiderivative and indefinite integral, Newton integral. 7. Riemann’s integral and its calculation, some applications in geometry and physics. 8. Numeric calculation of a definite integral. 9. Two- and more-functions, partial derivative and its use. 10. Probability, random variables. 11. Numerical characteritics of a random variable. 12. Basic distributions. 13. Random sampling, statistics