INMNAMAE Mathematics in Economics

Obchodně podnikatelská fakulta v Karviné
zima 2022
Rozsah
2/1/0. 6 kr. Ukončení: zk.
Vyučující
doc. Mgr. Jiří Mazurek, 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.
Omezení zápisu do předmětu
Předmět je určen pouze studentům mateřských oborů.
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.
Vyučovací jazyk
Angličtina
Předmět je zařazen také v obdobích zima 2023.