## INMNAMAT Mathematics in Economics

Summer 2016
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)
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
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.
Literature
required literature
• CHIANG, C.C. Fundamentals Methods of Mathematical Economics. New York: cGraw-Hill, Inc., 2000. ISBN 0-12-417890-1. info
recommended literature
• VINOGRADOV, V. Mathematics for Economists: Made Simple. Praha: Karolinum, 2010. ISBN 9788024616575. info
• PRICHET, G. D., SABER, J.C. Mathematics with applications in management and economics. IRWIN, Burr Ridge, Boston, Sydney, 2004. ISBN 0-256-09237-0. info
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.
The course is also listed under the following terms Summer 2015, Winter 2016, Summer 2017, Winter 2017, Summer 2018, Winter 2018, Summer 2019, Summer 2020, Summer 2021.
• Enrolment Statistics (Summer 2016, recent)