Czech

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Institute of Mathematics and Descriptive Geometry (MAT)

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).

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.

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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

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

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

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Larson R., Hostetler R.P., Edwards B.H.: Calculus (with analytic geometry). Brooks Cole, 2005 (EN)
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) (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) (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) (CS)
KOUTKOVÁ, Helena, Mill, Ivo: Základy pravděpodobnosti, Akademické nakladatelství CERM, s.r.o., Brno 2008. ISBN: 978-80-7204-574-7 (CS) (CS)
NOVOTNÝ, Jiří: Matematika I, Modul 1, Základy lineární algebry, Akademické nakladatelství CERM, s.r.o., Brno 2004. ISBN: 978-80-7204-748-2 (CS) (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) (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) (CS)

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