151-0801 – Mathematics A (MA Cžv)

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.

Taught in Czech only. It contains the following topics: 1. Linear algebra – Euclidean space, matrices, determinant. 2. Linear algebra – the inverse of the matrix, linear equations. 3. Functions of one real variable – definition, properties, graphs, inverse functions. 4. The limit of function – properties of limits, limits to infinity, one sided limits, definition of continuit, sequences, limits of sequences. 5. An introduction to the derivation – slope of a tangent line at a point, 6. Higher order derivations, l´Hospital´s rule. 7. Additional applications of derivation.

[4] Hoy M., Livernois J., McKenna Ch., Rees R., Stengos T. Mathematics for Economics. The MIT Press, London, 2011. [5] Tan T.S. Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011.

[4] Larson R., Falvo C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008. [5] Luderer B., Nollau V., Vetters K. Mathematical Formulas for Economists. Springer Verlag, third edition, 2007. [6] Simon C.P., Blume L. Mathematics for Economists. W.W. Norton & Company, New York-London, 2005.