## Mathematics

### Studijní plán: Finance a řízení - kombinovaná forma, platný pro studenty, kteří započali studium od ZS 2019/2020

Předmět Mathematics (MATfra) Katedra matematiky (KM) RNDr. Radek Stolín, Ph.D. ( stolin@vspj.cz ) Anglicky 6
Prezenční studium
Přednáška2 h
Cvičení2 h
Kombinované studium
Tutoriál / přednáška6 h
Cvičení12 h
Studijní plán Typ Sem. Kred. Ukon.
Finance a řízení - kombinovaná forma, platný pro studenty, kteří započali studium od ZS 2019/2020 P 1 6 kr. Z,ZK
Finance a řízení - platný pro studenty, kteří započali studium od ZS 2019/2020 P 1 6 kr. Z,ZK

#### Sylabus

• Basic facts from the propositional logic
• Functions and their properties
• Inverse function, circular functions
• Number sequences and their properties
• Limit of a function
• Derivative of a function
• L'Hospital's rule, asymptotes of a function
• Derivatives of order 1 and 2 and their applications
• Sketching the graph of a function, global extreme points of a function
• Indefinite integral, integration by parts, method of substitution
• Integration of rational functions
• Definite integral and its applications
• Applications of calculus in economics

#### Doporučená literatura

• ADAMS, R. A., ESSEX, CH. Calculus: a complete course. 9th edition. Toronto: Pearson, 2018.
ISBN 978-0-13-415436-7
• HOY, M., LIVERNOIS, J., MCKENNA, Ch., REES, R., STENGOS, T. Mathematics for Economics. 3rd edition. Cambridge: MIT Press, 2011. ISBN 978-0-262-01507-3

#### Anotace

The course aim is to equip students with basic knowledge of calculus of one real variable. Students should acquire basic computational skills relevant to the functions of one variable. Lectures are focused on the interpretation of the concepts of the differential and integral calculus. Exercises are devoted to solving practical problems.

Knowledge: The student knows basic definitions and theorems. He is able to sketch graphs of elementary functions using the differential calculus. He knows some applications of the integral calculus in economics.

Skills: Student can search for extremal values of functions of one variable and determine other specific properties related to the first or the second derivative of a given function. He also knows how to find an antiderivative to a given elementary function and how to evaluate a definite integral.

General competencies: Graduates are able to work with functions of one real variable, which is the basic description of dependence of variables. Moreover, they become familiar with applications of the differential and integral calculus in economics.

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