Celkem (h)	Př.	Cv.	Lab.	Sem.	Kurzy	Praxe	Stáže	Soustř.	Exkurze	Terén	SP	Konzultace	PV
Revision of secondary school mathematics – manipulations with algebraic expressions, powers, roots, exponential and logarithmic functions, logarithms, complex numbers, quadratic equations.	4	0	4	0	0	0	0	0	0	0	0	0	0	0
Real functions of a single variable: – set notation, number sets, –mappings and their properties, – functions of a single real variable, graph, linear and quadratic functions, indirect proportionality, absolute value, – monotonicity, even and odd functions, boundedness, periodic functtions, – one-to-one functions, composition of functions.	6	2	2	2	0	0	0	0	0	0	0	0	0	0
Elementary functions: – exponential and logarithmic functions, – power function, – trigonometric and inverse trigonometric functions.	4	2	2	0	0	0	0	0	0	0	0	0	0	0
Polynomials and rational functions: – operations with polynomials, Horner's scheme, roots of polynomials, factorization in the real and complex domain, – sign of polynomials a rational functions.	6	2	4	0	0	0	0	0	0	0	0	0	0	0
Limit and continuity of functions: – definition, types of limits, properties, continuity, evaluation.	4	2	2	0	0	0	0	0	0	0	0	0	0	0
Derivative of a function: – motivation, geometric and physical meaning, definition, – derivatives of elementary functions, basic formulae for derivatives, – higher order derivatives.,,	8	4	4	0	0	0	0	0	0	0	0	0	0	0
Applications of derivatives: – tangent and normal to the graph of function, – theorems on continuous and differentiable functions, – l'Hospital's rule, monotonicity and local extrema, convexity and concavity, inflection points, – asymptotes to the graph of function and investigation of behaviour of functions, – global extrema.	18	8	8	2	0	0	0	0	0	0	0	0	0	0
Approximation of functions by polynomials: – differential of function, linearization, – Taylor's and Maclaurin's formula, Maclaurin formulae of some elementary functions.	4	2	2	0	0	0	0	0	0	0	0	0	0	0
Indefinite integral: – definition, basic properties, some basic formulae, – integration by parts and substitution method, – decomposition of rational functions into partial fractions and their integration, – integration of special types of functions (trigonometric, algebraic).	12	6	6	0	0	0	0	0	0	0	0	0	0	0
Definite integral: – construction and its basic properties, – fundamental theorem of calculus, integration by parts and substitution method.	4	2	2	0	0	0	0	0	0	0	0	0	0	0
Geometric and physical applications of definite integral, – evaluation of area, length and volume, mass and coordinates of equilibrium.	6	2	2	2	0	0	0	0	0	0	0	0	0	0
Improper integral: – extension of definite integral to unbounded intervals and unbounded functions, – tests of convergence, absolute and conditional convergence, – gamma and beta functions.	8	4	4	0	0	0	0	0	0	0	0	0	0	0

Povinná:
Kuben, J. Diferenciální počet funkcí jedné proměnné. Skriptum. 1. vydání. Brno: Vojenská akademie v Brně, 2015. viii+333 s. Dostupné v knihovně UO pod číslem S-3854. ISBN 978-80-7231-991-6.
Kuben, J., Hošková, Š. Integrální počet funkcí jedné proměnné. Skriptum. 1. vydání. Brno: Univerzita obrany, 2004. vi+197 s. Dostupné v knihovně UO pod číslem S-368. ISBN 80-85960-75-3.
Kropáč, J., Kuben, J. Funkce gama a beta, transformace Laplaceova, Z a Fourierova. Skriptum. 3. vydání. Brno: Vojenská akademie v Brně, 2002. vi+136 s. Dostupné v knihovně UO pod číslem S-731/B.

Doporučená:
Kuben, J. Differential calculus for functions of a single variable. Skriptum. 1. vydání. Brno: Univerzita obrany, 2012. x+321 s. Dostupné v knihovně UO pod číslem S-3573. ISBN 978-80-7231-849-0. Elektronická verze do-stupná z https://moodle.unob.cz/course/view.php?id=356 [cit. 2020-07-23.2].
Kuben, J. Integral calculus for functions of a single variable. Skriptum. 1. vydání. Brno: Univerzita obrany, 2011. x+227 s. Dostupné v knihovně UO pod číslem S-3146. ISBN 978-80-7231-798-1. Elektronická verze dostupná z https://moodle.unob.cz/course/view.php?id=356 [cit. 2020-07-23].