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Mathematics 1

Type of study Bachelor
Language of instruction English
Code 310-2301/01
Abbreviation Math 1
Course title Mathematics 1
Credits 5
Coordinating department Department of Mathematics and Descriptive Geometry
Course coordinator RNDr. Jan Kotůlek, Ph.D.

Osnova předmětu

1 Linear algebra. Operations with matrices. Determinants. Properties of determinants.
2 Rank of a matrix. Inverse matrix.
3 Solution of linear equations. Frobenius theorem. Cramer's rule.
4 Gaussian elimination algorithm.
5 Real functions of one real variable. Definitions, graph. Function bounded, monotonous,
even, odd, periodic. One-to-one function, inverse and composite functions.
6 Elementary functions.
7 Limit of a function. Continuous and discontinuous functions.
8 Differential calculus of one variable. Derivative of a function, its geometrical and
physical applications. Rules of differentiation.
9 Derivatives of elementary functions.
10 Differential functions. Derivative of a function defined parametrically. Derivatives of
higher orders. L'Hospital's rule.
11 Use of derivatives to detect monotonicity, convexity and concavity features.
12 Extrema of functions. Asymptotes. Graph of a function.
13 Analytic geometry in E3. Scalar, cross and triple product of vectors and their properties.
14 Equation of a line. Equation of a plane. Relative positions problems.
Metric or distance problems.

E-learning

Povinná literatura

Neustupa J.: Mathematics I. ČVUT, Praha 2004.
Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0.
Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.

Doporučená literatura

Neustupa J.: Mathematics I. ČVUT, Praha 2004.
Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0
Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.