# OPF:INMNAMAT Mathematics in Economics - Course Information

## INMNAMAT Mathematics in Economics

**School of Business Administration in Karvina**

Winter 2018

**Extent and Intensity**- 2/1/0. 5 credit(s). Type of Completion: zk (examination).
**Teacher(s)**- Mgr. Jiří Mazurek, Ph.D. (lecturer)

prof. RNDr. Jaroslav Ramík, CSc. (lecturer)

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. **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**- there are 7 fields of study the course is directly associated with, display
**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**- Functions of one real variable

Functions of one real variable are introduced as well as their properties and economic applications: supply, demand, equilibrium under perfect competition. Differential calculus, Taylor theorem and Taylor and Maclaurin polynomials are explained. The differential calculus is applied to finding function extremes and monotonicity, economic applications include 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.

Functions of two real variables

The function of two variables is introduced. A domain of a function of two real variables, partial derivatives, total differential of the first and second order and a tangent plane are explained. Applications include finding local and bounded extremes with the use of Weierstrass extreme value theorem and the method of Lagrange multipliers, and finding an increase of Cobb-Douglas production function by the total differential.

Indefinite and definite integral of one real variable

Indefinite and definite integral, and Newton-Leibniz formula, are introduced. Integration methods including per partes method, partial fractions and substitutions are explained. Integral calculus is applied to estimations of total costs and total revenues, a calculation of an area of regions and a volume of solids, or consumer and producer surplus under perfect competition.

Infinite number and function series

Infinite number series and their convergence is explained. Limiting criteria and integral criterion of convergence of positive infinite series is shown, also alternating series are discussed. Infinite function series are introduced as a generalization to number series.

Geometric and power function series, Taylor series and convergence of function series are explained.

Differential equations

Ordinary differential equations are introduced, general and particular integral is explained, a method of separation of variables is shown. Linear differential equations of the first order and homogenous differential equations are explained.

- Functions of one real variable
**Literature**- CHIANG, A. C., WAINWRIGHT, K.
*Fundamental Methods of Mathematical Economics, 4th edition*. New York:McGraw-Hill, 2005. ISBN 978-0070109100. info

*required literature*- KLEIN, M.
*Mathematical Methods for Economics, 2nd Edition*. Pearson New International Edition, 2013. ISBN 978-1292039183. info - ASANO, A.
*An Introduction to Mathematics for Economics*. Canbridge University Press, 2012. ISBN 978-0521189460. info - DOWLING, E.
*Schaum's Outline of Introduction to Mathematical Economics, 3rd Edition*. McGraw-Hill Education, 2011. ISBN 978-0071762519. info

*recommended literature*- CHIANG, A. C., WAINWRIGHT, K.
**Teaching methods**- Lecture with presentation in Power-point
**Assessment methods**- Grade
**Language of instruction**- English
**Further Comments**- The course can also be completed outside the examination period.
**Teacher's information**- attendance in seminars 70 %, final written exam

- Enrolment Statistics (Winter 2018, recent)
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