151-0401/03 – Mathematics B (MBKS)

Knowledge, comprehension The student will be able to... - solve the systems of linear equations by using the Gaussian elimination and Cramer's rule, - control basic terminology and related applications in economics, - write the systems of linear equations with the help of the matrix notation - explain the concept of the primitive function and the indefinite integral, - explain and to control the basic rules, formulas and techniques of integration - define and to calculate the definite integral with the help of the Newton-Leibniz formula, - explain the validity of the geometric application (quadrature only), - present at least one application of the definite integral in economics - define the real function of two real variables, - give examples of basic functions of two variables (especially the constant, linear and Cobb-Douglass function), - give examples of using the functions of two variables in economics, - find the domain of the functions of two variables and its graphical visualization, - find the level curves of basic functions of two variables and to know the economic interpretation, - explain the concept of the homogenous functions of order 's' and to present the geometric and economic interpretation - define and to calculate the partial derivatives with the help of rules and formulas, - define the local extremes of functions of two variables, - interpret the local extremes in economics, - apply the partial derivatives for determining the existence and the nature of local extremes, - discuss the existence and nature of local extremes by means of their definition, - find the constrained extremes (the method of substitution, Lagrange's multiplier) - determine the type of a basic ordinary first-order differential equation, - solve basic types of first-order differential equations with the help of the direct integration, the constant variation and with the method of undetermined coefficients, - solve the basic second-order linear differential equations with the constant coefficients and with the special right-hand side by means of the method of undetermined coefficients, - outline at least one basic interpretation of the first- and second-order differential equations in economics - control and to explain the basic rules and formulas of the difference calculus, - explain the connection of the first- and second-order difference sign in connection with monotonicity and its dynamics, - determine the monotonicity of sequences with the help of the first- and second-order difference, - know the relationship between the summation and difference, - define the first- and second-order linear difference equations, - explain the existence of general first- and second-order linear difference equations with constant coefficients, - solve the first- and second-order linear difference equations with constant coefficients and with the special right-hand side, - find the closed form of basic finite sums with the help of the first-order linear difference equations, - present basic applications of difference equations in economics

Aims of the subject are... - to get acquainted with further basic concepts of caluclus, - to develop the logical thinking and argumentation skills, - to point out the basic application context of mathematics and economics.

Šalounová D., Poloučková A.: Úvod do lineární algebry. VŠB-TU, Ostrava (2002) Genčev M.: Cvičebnice ke kurzu Matematika A. SOT, Ostrava (2013) Moučka J., Rádl P.: Matematika pro studenty ekonomie. Grada, Praha (2010) Tan T.S.: Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont (2011)

Studenti mají ke každému učivu test, mohou si tak sami ověřit, zda probranému učivu porozuměli či nikoliv. Také mají vzor závěrečné písemné zkoušky, kde si mohou opět vyzkoušet, zda by u zkoušky uspěli či nikoliv.