## Mathematics A

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code Number of ECTS Credits Allocated Type of Course Unit * Level of Course Unit * Year of Study * 151-0300/04 5 ECTS credits Compulsory First Cycle First Year Winter Semester Face-to-face Czech, English, German, Spanish There are no prerequisites or co-requisites for this course unit ARE30 Ing. Orlando Arencibia Montero, Ph.D. S1A20 prof. RNDr. Dana Šalounová, Ph.D. RUC05 RNDr. Pavel Rucki, Ph.D. KOZ214 Ing. Mgr. Petr Kozel, Ph.D. ZAH0001 Marek Zahradníček GEN02 Mgr. Marian Genčev, Ph.D. Taught in Czech. The subject continues fulfilling general methodical and professional goals of Mathematics, i.e. to train the rational thinking and the ability to conceive and work with quantitative information concerning the real world. This is being done especially by mathematization of the practical as well as theoretical economic problems. This subject supplies the students’ education with realms of higher Mathematics which is applicable namely to the creation and investigation of economic models. Knowledge • Define the function of one variable. • Find the domain and range and basic properties. • Draw graphs of elementary functions. • Compute limits and derivates of functions. • Find the properties of no elementary functions a draw theirs graphs. • Obtain easier imagine about economic functions. • Order knowledge about vectors in the plain. • Identify the types of matrices. • Solve the system of linear equations. Comprehension • Express economic dependences using a mathematical function. • Explain the slope of a function. • Restate the terms “concavity” and “convexity” into the “degressive” and “progressive”. • Generalise the functions on the dependences in the real live. • Express knowledge of vectors to the space. Applications • Relate economic and mathematical functions. • Discover the tools suitable for describing of dependences in economics and other sciences. • Develop the technique of graphs drawing. • Apply knowledge of linear algebra in economics, e.g. traffic problems, structural analysis. • Solve basic problems of linear programming. 1. Real sequences - definition, properties, arithmetic sequence, geometric sequence, limit of a sequence. 2. Functions of one real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing), inverse functions, composition of functions. 3. The limits of functions – properties of limits, limits to infinity, one sided limits, definition of continuity, continuity on an interval. 4. An introduction to the derivate – slope of a tangent line at a point, derivative, equation of a tangent line and normal line to a curve at a point, techniques of differentiation, higher order derivations, l´Hospital´s rule. 5. Linear algebra – matrices, addition and multiplication of matrices, rank of a matrix, determinant, the inverse of the matrix, matrix equations. [1] SYDSAETER, K., HAMMOND, P. J. Mathematics for Economics Analysis. Pearson, 2002, ISBN 978-81-7758104-1. [2] HOY, M., LIVERNOIS, J., MCKENNA, Ch., REES, R., STENGOS, T. Mathematics for Economics. The MIT Press, London, 3rd edition, 2011, ISBN 978-0-262-01507-3. [3] TAN, T.S. Single variable calculus: early transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011, ISBN 978-1-4390-4600-5. Povinná literatura v českém jazyce: ~~~~~~~~~~~~~~~~~~~~~~~~~~~ [1] GENČEV, M., HRUBÁ, J., PULCEROVÁ, S., RUCKI, P. Matematika A. SOT, vol. 5, Ostrava: VŠB-TU Ostrava, 2013. ISBN 978-80-248-3154-1. [2] GENČEV, M., RUCKI, P. Cvičebnice z matematiky nejen pro ekonomy I. SOT, vol. 32, Ostrava: VŠB-TU Ostrava, 2017, ISBN 978-80-248-4100-7. [3] Studijní opory s převažujícími distančními prvky pro předměty teoretického základu studia, http://www.studopory.vsb.cz [1] LARSON, R. Elementary Linear Algebra. Brooks/Cole Cengage Learning, Belmont, 8th edition, 2016, ISBN 978-1305658004. [2] LUDERER, B., NOLLAU, V., VETTERS, K. Mathematical Formulas for Economists. Springer Verlag, 3rd edition, 2006, ISBN 978-3540469018. Doporučená literatura v českém jazyce: ~~~~~~~~~~~~~~~~~~~~~~~~~~~ [1] POLOUČKOVÁ, A., ŠALOUNOVÁ, D. Diferenciální počet I. VŠB–TU Ostrava, 2003, ISBN 80-7078-904-2. [2] POLOUČKOVÁ, A., ŠALOUNOVÁ, D. Úvod do lineární algebry. VŠB-TU Ostrava, 2002, ISBN 80-248-0199-X. [3] COUFAL, J., KLŮFA, J. Matematika pro ekonomické fakulty 1. 1. Vydání Ekopress, Praha 2000. ISBN 80-86119-30-0. [4] KAŇKA, M., HENZLER, J. Matematika pro ekonomické fakulty 2. 1. Vydání Ekopress, Praha 2000. ISBN 80-86119-31-9. [5] REKTORYS, K. Přehled užité matematiky. Prometheus, Praha, 2009. ISBN 978-80-7196-180-2. Doporučená literatura v cizím jazyce: ~~~~~~~~~~~~~~~~~~~~~~~~~~~ [6] HOY, M., LIVERNOIS, J., MCKENNA, Ch., REES, R., STENGOS, T. Mathematics for Economics. The MIT Press, London, 3rd edition, 2011, ISBN 978-0-262-01507-3. [7] TAN, T.S. Single variable calculus: early transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011, ISBN 978-1-4390-4600-5. [8] LARSON, R. Elementary Linear Algebra. Brooks/Cole Cengage Learning, Belmont, 8th edition, 2016, ISBN 978-1305658004. [9] LUDERER, B., NOLLAU, V., VETTERS, K. Mathematical Formulas for Economists. Springer Verlag, 3rd edition, 2006, ISBN 978-3540469018. Lectures, Individual consultations, Tutorials, Other activities Graded credit Graded credit 100 (100) 51 Zápočtová písemka Written test 100 51