Course detail

# Mathematics

FAST-AA001Acad. year: 2018/2019

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.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

After the course, students should understand the basics of linear algebra, vector algebra, differential and integral calculus of functions of one variable, differential calculus of functions of several variables and 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.

Recommended optional programme components

Not applicable.

Recommended or required reading

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 – lectures, seminars.

Assesment methods and criteria linked to learning outcomes

Abilities leading to successful solution of some typical classes of differential equations as well as necessary theoretical knowledge and its application will be positively estimated. The final evaluation (examination) depends on assigned points (0-100 points), 30 points is maximum points which can be assigned during seminars. Final examination is in written form (estimated by 0-70 points ).

Language of instruction

Czech

Work placements

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

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.

Classification of course in study plans

• Programme B-P-C-APS (N) Bachelor's

branch APS , 1. year of study, winter semester, 3 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

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 hours, compulsory

Teacher / Lecturer

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