151-0502/02 – Mathematics B (MathB)

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) - recognize the type of a basic ordinary first-order differential equation, - explain the existence and the solution form of the first- and second-order differential equations, - 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, - explain the solution form of homogeneous 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.

Stewart J.S.: Calculus - Concepts and Contexts. Cengage Learning (2010) Canuto C., Tabacco A.: Mathematical Analysis I. Springer Verlag (2008) Luderer B., Nollau V., Vetters K.: Mathematical Formulas for Economists. Springer Verlag, 3rd ed. (2007) Tan T.S.: Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont (2011)

Credit (written form - test) - max. 40 pts, - min. 20 pts Examination (written and oral) - written exam (written test) - max. 42 pts, - min. 22 pts - oral exam (open-book) - max. 18 pts, - min. 9 pts