151-0560 – Basic Mathematics (BasicM)

The aim of the subject is to get acquainted with the basic knowledge of advanced mathematics, which is necessary for further studies of quantitative methods in economics. The subject’s structure and nature themselves have their importance as they help to develop logical thinking as well as the ability to enunciate thoughts accurately and to give clear argumentation when solving the practical problems. After successful and active graduation of subject • will know: count limit of function, derivate of function, count with matrices, count integral indefinite and definite, • profit: basic knowledge from differential calculus, from linear algebra and from integral calculus, • will be able: use mathematics as instrument for better comprehension of economy.

1. Functions of one real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing), inverse functions. 2. The limits of functions – properties of limits, limits to infinity, one sided limits, definition of continuity, continuity on an interval. 3. 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. 4. Linear algebra – linear dependence of vectors, linear independence of vectors, matrices, addition and multiplication of matrices, determinant, the inverse of the matrix, matrix equations. 5. The indefinite integral – definition and properties, basic integration rules, methods of integration: integration by substitution, integration by parts. 6. The definite integral – definition and properties, the Newton-Leibniz formula.

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Goldstein, L., Lay, D., Schneider, D. and Asmar, N. Calculus and Its Applications. Pearson, 2010, ISBN: 978-0-3-21571304. Larson, R., Falvo, C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008. Luderer B., Nollau V., Vetters K. Mathematical Formulas for Economists. Springer Verlag, third edition, 2007. Sydsaeter, K., Hammond, P. J. Mathematics for Economics Analysis. Pearson Education Limited, 2008, ISBN 978-0-273-71324-1. Tan T.S. Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011.