Basics of mathematics in business 2600-DSFRz1PMB
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.
Total number of hours – 100
Classes (including assessment) – 40 hours
Own work – solving tasks – 50 hours
Preparation for the colloquium – 10 hours
Type of course
Mode
Course coordinators
Learning outcomes
K_W01 – The student knows and understands in-depth research methodology and terminology in the field of management and quality sciences and in complementary disciplines (economics and finance, legal sciences), in particular the use of mathematical analysis and matrix calculus.
K_W03 – The student knows and understands in-depth economic theories and models (especially those constructed using mathematical methods) regarding the functioning of organizations and the entire economy.
K_U02 – The student is able to correctly interpret technological, social, political, legal, economic and ecological processes and phenomena and their impact on the functioning of the organization and the entire economy, using the appropriate selection of computational methods.
K_K01 – The student is ready to assess and critically approach situations and phenomena related to the functioning of the organization, sector and the entire economy using mathematical models.
Assessment criteria
During the semester, students write two colloquia consisting of open computational tasks; To pass, it is required to obtain at least 60% of points in each test
Bibliography
Basic:
Ostoja-Ostaszewski A., Matematyka w ekonomii. Modele i metody, Tom 1 i 2, PWN 2006
Additional:
Piasecki K., Anholcer M., Echaust K., e-Matematyka wspomagająca ekonomię, C. H. Beck 2006.
Bażańska T., Nykowska M., Matematyka w zadaniach dla wyższych zawodowych uczelni ekonomicznych, Oficyna Wydawnicza Branta, 2007
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: