Course detail

Mathematics

FAST-BAA014Acad. year: 2021/2022

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

Mgr. et Mgr. Jan Šafařík, Ph.D.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

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).

Prerequisites

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.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

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

Work placements

Not applicable.

Aims

The students should learn about the basics of linear algebra, solutions to systems of linear algebraic equations, calculus, theory of probability and statistics.

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

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

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme BPC-APS Bachelor's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Mgr. et Mgr. Jan Šafařík, Ph.D.

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

Mgr. et Mgr. Jan Šafařík, Ph.D.

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