Course Details

Mathematics

Academic Year 2023/24

BAA014 course is part of 1 study plan

​ BPC-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.

Credits

3 credits

Language of instruction

Czech

Semester

winter

Course Guarantor

Mgr. et Mgr. Jan Šafařík, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

course-unit credit and examination

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.

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).

Basic Literature

LARSON, Ron, HOSTETLER, Rober, EDWARDS Bruce: Calculus With Analytic Geometry, 8th edition, Brooks Cole, 2005.  ISBN: 978-0618502981 (en)
NOVOTNÝ, Jiří: Matematika I, Modul 1, Základy lineární algebry, Akademické nakladatelství CERM, s.r.o., Brno 2004. ISBN: 978-80-7204-748-2 (cs)
TRYHUK, Václav, DLOUHÝ, Oldřich: Matematika I, Modul GA01–M01, Vybrané části a aplikace vektorového počtu, Akademické nakladatelství CERM, s.r.o., Brno 2004. ISBN: 978-80-7204-526-6 (cs)
DLOUHÝ, Oldřich, TRYHUK, Václav: Matematika I, Diferenciální počet funkce jedné reálné proměnné}, Akademické nakladatelství CERM, s.r.o., Brno 2008. ISBN: 978-80-7204-982-0 (cs)
DANĚČEK, Josef, DLOUHÝ, Oldřich, PŘIBYL, Oto: Matematika I, Modul 7, Neurčitý integrál, Fakulta stavební VUT, Akademické nakladatelství CERM, Brno 2007. ISBN: 978-80-7204-524-2 (cs)
DANĚČEK, Josef, DLOUHÝ, Oldřich, PŘIBYL, Oto: Matematika I, Modul 8, Určitý integrál, Fakulta stavební VUT, Akademické nakladatelství CERM, Brno 2007. ISBN: 978-80-7204-525-9 (cs)
TRYHUK, Václav, DLOUHÝ, Oldřich: Matematika I, Diferenciální počet funkcí více reálných proměnných, Akademické nakladatelství CERM, s.r.o., Brno 2004. ISBN: 80-214-2776-0 (cs)
KOUTKOVÁ, Helena, Mill, Ivo: Základy pravděpodobnosti, Akademické nakladatelství CERM, s.r.o., Brno 2008. ISBN: 978-80-7204-574-7 (cs)

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.

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

https://www.vut.cz/en/students/courses/detail/273714

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