Studijní plán:

Sylabus

• Sets, propositional calculus, basic elementary functions and their graphs.
• Real function of one real variable. Basic definitions: domain and range, operations with functions, composite function, inverse function.
• Limit at a point, continuity of a function at a point. Basic properties of limits.
• Derivative. Physical meaning of the first derivative (velocity), geometrical meaning (slope, tangent line, normal to a graph).
• Mean value theorems (Rolle, Lagrange, Cauchy). The l'Hospital rule. Asymptots to a graph.
• Monotony of a function, local extreme values. Concave and convex functions, inflection points of the graph.
• Sketching the graph of a function, global extreme values.
• Approximation of the function: differential, the Taylor polynomial.
• Systems of algebraic linear equations, matrices, linear independence of rows in a matrix, rank of a matrix, Gaussian elimination method.
• Matrix algebra: linear combination of matrices, matrix multiplication. Determinants: definition, evaluating determinants of degree 2 and 3.
• Matrix inverse. Cofactor, expanding a determinant about a row or a column, row or column transformations of determinants. Calculating a matrix inverse by determinats or by the Jordan elimination.
• Systems of linear quations with a general matrix. Solvability (Frobenius theorem), solving a system by the Gaussian elimination.
• Basics of linear programming.
• Vector spaces: arithmetic vector space, vector space of functions on an interval.

Doporučená literatura

• HOY, Michael, LIVERNOIS, John, MCKENNA, Chris, REES, Ray and STENGOS, Thanasis. Mathematics for Economics, 3rd edition, MIT Press, 2011, 958 pp., ISBN978-0-262-01507-
• THOMPSON, Silvanus P., GARDNER, Martin. Calculus Made Easy. St. Martin´s Press, 1998, 243 pp., ISBN 0312185480.
• STRANG, Gilbert. Introduction to linear algebra, 4th edition. Wellesley Cambridge Press, 2009, 584 pp., ISBN 0980232716.
• STRANG, Gilbert. Calculus, 2th edition. Wellesley Cambridge Press, 20, 716 pp., ISBN 0980232740.

Anotace

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