# OPF:INMNAMAT Mathematics in Economics - Course Information

## INMNAMAT Mathematics in Economics

**School of Business Administration in Karvina**

Summer 2015

**Extent and Intensity**- 2/1/0. 5 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- prof. RNDr. Jaroslav Ramík, CSc. (lecturer)

Mgr. Radmila Krkošková, Ph.D. (seminar tutor)

doc. Mgr. Jiří Mazurek, Ph.D. (seminar tutor) **Guaranteed by**- prof. RNDr. Jaroslav Ramík, CSc.

Department of Informatics and Mathematics – School of Business Administration in Karvina

Contact Person: Mgr. Radmila Krkošková, Ph.D. **Prerequisites**(in Czech)- K absolvování předmětu nejsou vyžadovány žádné podmínky a předmět může být zapsán nezávisle na jiných předmětech.
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Banking (programme OPF, N_HOSPOL)
- Economy of Enterprise in Trade and Services (programme OPF, N_EKOMAN)
- Managerial Informatics (programme OPF, N_SYSINF)

**Course objectives**- The course Mathematics in economics in master's study programme follows the course Quantitative methods in bachelor's study programme. It makes the participants acquainted with further knowledge and methods of differential and integral calculus, and the introduction to differential equations including their application in economics. The aim of the course is to cultivate approach to problem solution particularly in a variety of economic branches and to enable insight into their essence.
**Syllabus**- 1. Function of one variable

2. Introduction to differential calculus of one real variable

3. Course of a function of one real variable

4. Function of two variables

5. Local and bounded extremes of a function of two variables

6. Indefinite integral of one real variable

7. Special substitutions in the indefinite integral

8. Definite integral of one real variable

9. Applications of the definite integral

10. Infinite number series

11. Infinite function series

12. Introduction into ordinary differential equations

13. Linear differential equations

1. Functions of one real variable

Algebraic functions, transcendent functions, polynomials, decomposition of a polynomial into product of its roots. Economic applications: supply, demand, equilibrium under perfect competition..

2. The introduction to differential calculus of one real variable

Difference, derivative, differential. Taylor theorem, Taylor and Maclaurin polynomials. Economic applications: rate of a change of a function, function elasticity, substitution of a function by a polynomial of the n-th degree, marginal costs, marginal revenues, minimization of average costs, maximization of total revenue, maximization of profit.

3. The course of a function of one real variable

Economic applications: function of total, average and marginal costs and revenues, minimization of costs, maximization of revenue and profit, relationship between average costs and marginal costs under perfect competition..

4. The function of two real variables

Domain of a function of two real variables, partial derivatives, total differential of the first and second order, tangent plane.

5. Local and bounded extremes of a function of two variables

Weierstrass extrem value theorem, the method of Lagrange multipliers, Economic applications: Cobb-Douglas production function, maximization of revenue and profit, minimization of costs under perfect competition.

6. Indefinite integral of one real variable

Method per partes, substitution, integration of partial fractions. Economic applications: total costs and total revenues.

7. Special substitutions in the indefinite integral

Integration of rational, exponential, logarithmic and goniometric functions.

8. Definite integral of one real variable

Riemann integral, Newton-Leibniz formula, improper integral.

9. . Applications of the definite integral

Calculation of area of regions and volume of solids. Economic applications: consumer and producer surplus under perfect competition.

10. Infinite number series

Infinite number series and their convergence. Limiting criteria and integral criterion of convergence of positive infinite series. Alternating series.

11. Infinite function series

Geometric and power function series, Taylor series. Convergence of series.

12. Introduction into ordinary differential equations

General and particular integral, separation of variables.

13. Linear differential equations

Linear differential equations of the first order, homogenous differential equations.

- 1. Function of one variable
**Literature****Teaching methods**- Skills demonstration

Seminar classes **Assessment methods**- Written exam

Written test **Language of instruction**- English
**Further comments (probably available only in Czech)**- The course can also be completed outside the examination period.
**Teacher's information**- test, 70% attendance at the seminars, exam test, form of the exam: written.
Activity Difficulty [h] Ostatní studijní zátěž 61 Přednáška 26 Seminář 13 Zkouška 40 **Summary**140

- Enrolment Statistics (Summer 2015, recent)
- Permalink: https://is.slu.cz/course/opf/summer2015/INMNAMAT