(in Polish) Podstawy matematyki w biznesie 2600-LFBRz1PMB

LECTURE:
1. Finite summation and functions of one variable: calculation procedure and arithmetic properties of the generalized sum; construction of a function given by a formula, composition of functions; properties of functions: monotonicity, concavity and intuitive concept of continuity.
2. Continuity and derivative of functions: limit of functions at a point, continuous functions and their properties (Darboux property and its application to approximate solution of equations); concept and definition of the derivative of a function, calculation of derivatives (including the derivative of a composition of functions), interpretation of the derivative as the rate of change, economic application (marginal analysis, flexibility of functions);
3. Basics of integral calculus: the concept of antiderivative function, definition and determination of indefinite integral (methods of integration by parts and change of variables), definite integral (in Riemann's sense), basic theorem of integral calculus; determining the area under the curve and bounded by the curves; economic application (e.g. calculating revenue, profit, production volume in a specific time).
4. Matrix calculus and systems of linear equations: matrices, matrix multiplication, matrix inverse, matrix determinant;
application of matrix calculus in management (communication matrix, transition matrix); systems of linear equations as models of economic problems; methods for solving systems of linear equations.
5. Functions of many variables: the concept of functions of many variables, graph of a function of two variables; calculation of partial derivatives, importance of gradient of functions; determining local extrema of functions of many variables.

CLASSES:
1. Calculation of limits of sequences and limits of functions at a point and at infinity, improper limits, checking the continuity of functions,
2. Determining derivatives of elementary functions, products and quotients of functions and composition of functions.
3. Searching for local and global extremes of functions of one variable, examining monotonicity and concavity of functions.
5. Determining the indefinite integral of elementary functions, integration by substitution and by parts, determining the integration constant from boundary conditions.
6. Calculating definite integrals, determining the area under the curve and bounded by the curves.
4. Matrices, matrix multiplication, determining the determinant, determining the inverse matrix.
5. Solving systems of linear equations using the inverse matrix, Cramer's formulas and Gauss-Jordan elimination.
6. Calculation of partial derivatives of functions of many variables; determining local extrema of functions of two variables.

Estimated number of hours of independent student work:
- approximately 60 hours of preparation for classes,
- approximately 15 hours of preparation for the final assessment.