INMNAMAE Mathematics in Economics

Obchodně podnikatelská fakulta v Karviné
zima 2023
Rozsah
2/1/0. 6 kr. Ukončení: zk.
Vyučující
Mgr. Radmila Krkošková, Ph.D. (přednášející)
Garance
doc. Mgr. Jiří Mazurek, Ph.D.
Katedra informatiky a matematiky – Obchodně podnikatelská fakulta v Karviné
Kontaktní osoba: Mgr. Radmila Krkošková, Ph.D.
Rozvrh
St 13:55–15:30 A423
  • Rozvrh seminárních/paralelních skupin:
INMNAMAE/01: St 15:35–16:20 A423, R. Krkošková
Předpoklady
Elementary knowledge of algebra and mathematical analysis.
Omezení zápisu do předmětu
Předmět je určen pouze studentům mateřských oborů.

Předmět si smí zapsat nejvýše 50 stud.
Momentální stav registrace a zápisu: zapsáno: 29/50, pouze zareg.: 0/50
Mateřské obory/plány
Cíle předmětu
The objective of the course is to provide a student a solid mathematical foundations necessary for other courses in economics.
Výstupy z učení
A student will be able to understand functions of one and two real variables, find a maximum, minimum, monotonicity and a domain of a function, plot its graph, and solve simple equations.
Osnova
  • 1. Real function of one real variable
    Algebraic functions, transcendent functions, polynomials, roots of the polynomial. Applications in economics: supply and demand functions, equilibrium point in perfect competition, derivative of function, differential Taylor´s theorem, Applications in economics: change rate of function, elasticity of function, approximation of function by polynomial of n-th power, marginal costs, marginal revenues. Course and shape of function, minimization of costs, revenues and profit.
    2. Real function of two real variables
    Domain of definition, domain of function of two variables, partial derivative, total differential first and second order, tangential hyperplane. Local and constrained extremum of function of two variables. Theorem of Weierstrass of revenues and profit, Lagrange multipliers theorem, method of variable coefficients. Cobb-Douglas production function, maximization of revenues and profits, minimization of costs under perfect competition.
    3. Indefinite integral (antiderivative) of function of one real variable
    Per-partes integration method, substitution method, integration of partial fractions. Applications in economics: total costs and total revenues. Integration of rational, exponential, logarithmic and goniometric functions.
    4. Definite integral of function of one real variable
    Riemann integral, Newton-Leibniz formula, improper integral. Applications in economics: calculation of area and volume of geometrical body. Applications in economics: surplus of consumer and producer under perfect competition.
    5. Infinite number series and function series
    Infinite number successions and series and their convergence. Geometric and power series. Applications in economics: sum of infinite geometric series.
    6. Ordinary differential equations
    General and particular solution, separation of variables. Linear differential equation of the first order, homogenous differential equation.
Literatura
    povinná literatura
  • CHIANG, C.C. Fundamentals Methods of Mathematical Economics. New York: cGraw-Hill, Inc., 2000. ISBN 0-12-417890-1. info
    doporučená literatura
  • 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
Výukové metody
Lecture, class discussion, seminar
Metody hodnocení
Final written assignment: 80% (80 points) Activity: 10% (10 points) Homeworks: 10% (10 points) To pass the subject a student needs at least 60% (60 points).
Vyučovací jazyk
Angličtina
Další komentáře
Studijní materiály
Předmět je zařazen také v obdobích zima 2022, zima 2024.