Course Details

Mathematics

Academic Year 2023/24

AA001 course is part of 1 study plan

B-P-C-APS (N) / APS Winter Semester 1st year

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.

Course Guarantor

Institute

Objective

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

Knowledge

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).

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

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.

Language of instruction

Czech

Credits

3 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

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

Offered to foreign students

Not to offer

Course on BUT site

Lecture

13 weeks, 2 hours/week, elective

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 weeks, 1 hours/week, compulsory

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