Czech

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

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Basic secondary-school mathematics. Graphs of essential elementary functions (powers and roots, quadratic function, direct and indirect proportion, absolute value, trigonometric functions) and the basic properties of such functions. Simplification of algebraic expressions. Definition of a geometric vector and basics of 3D analytic geometry (parametric equations of a straight line, dot product of vectors and its applications to metric and positional problems). Identifying the the types and basic properties of conics, sketching graphs of conics).

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1. Real function of one real variable, explicit and parametric definition of a function. Composite function and inverse to a function.
2. Some elementary functions, inverse trigonometric functions. Hyperbolic functions. Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real numbers.
3. Rational functions. Sequence and its limit.
4. Limit of a function, continuous functions, basic theorems. Derivative of a function, its geometric and physical applications, differentiating rules.
5. Derivatives of composite and inverse functions. Differential of a function. Rolle and Lagrange theorem.
6. Higher-order derivatives, higher-order differentials. Taylor theorem.
7. L`Hospital's rule. Asymptotes of the graph of a function. Sketching the graph of a function.
8. Basics of matrix calculus, elementary transformations of a matrix, rank of a matrix. Solutions to systems of linear algebraic equations by Gauss elimination method.
9. Second-order determinants. Higher-order determinants calculated by Laplace expansion. Rules for calculating with determinants. Cramer's rule of solving a system of linear algebraic equations.
10. Inverse to a matrix. Jordan's method of calculation. Matrix equations. Real linear space, base and dimension of a linear space. Linear spaces of arithmetic and geometric vectors.
11. Eigenvalues and eigenvectors of a matrix. Coordinates of a vector. Dot and cross product of vectors, calculating with coordinates.
12. Mixed product of vectors. Plane in E3. Straight line in E3, positional problems.
13. Metric problems in E3. Surfaces in E3.

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After the course, students should understand the basics of calculus of functions of one variable and the basic interpretations of some of the concepts. They should master differentiating and sketching the graph of a function.
They should know how to perform operations with matrices, elementary transactions, calculate determinants, solve systems of algebraic equations using Gauss elimination method.

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)
STEIN, S. K.: Calculus and analytic geometry. New York, 1989. (EN)

DANĚČEK, J. a kolektiv: Sbírka příkladů z matematiky I. Akademické nakladatelství CERM, s.r.o. Brno, 2003. (CS)
DLOUHÝ, O. - TRYHUK, V.: Matematika I, Diferenciální počet funkce jedné reálné proměnné. CERM, s.r.o. Brno, 2009. (CS)
Kolektiv: Elektronické studijní opory předmětu BA06. FAST VUT, 2004. [https://intranet.fce.vutbr.cz/pedagog/predmety/opory.asp] (CS)
Kolektiv: Sbírka příkladů z matematiky I. Akademické nakladatelství CERM Brno, 2003. (CS)
Kolektiv: Studijní opory předmětu BA01, moduly M07,08,09,10. FAST VUT, Brno, 2004. [https://intranet.fce.vutbr.cz/pedagog/predmety/opory.asp] (CS)
NOVOTNÝ, J.: Základy lineární algebry. CERM, 2004. (CS)