MATHEMATICS IN ECONOMICS – Syllabus and General Information

5 CREDITS, SUMMER SEMESTER


Aim of the course:

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.

Requirements

70% attendance at the seminars, two tests (for 30 points and 70 points). Form of the exam: written.

Content

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:


  * BRADLEY, T., PATTON, P. Essentials Mathematics for Economics and Business. West Susex: John
Wiley & Sons Ltd, 1998. ISBN 0-471-97511-7.
  * CHIANG, C.C. Fundamental Methods of Mathematical Economics. New York: McGraw-Hill, Inc., 2000.
ISBN 0-12-417890-1.