Mathematics for Business 2600-BM-MATHFB

1. Repetition of secondary school mathematics.

2. Matrices, matrix multiplication, calculating the determinant, calculating the inverse of a matrix.

3. Systems of linear equations. Solving systems of linear equations using the inverse matrix, Cramer's rule, and Gauss-Jordan elimination. The method of linear programming as an application of the theory.

4. Sequences of real numbers, calculating limits of sequences, the limit „e”; the notion of the sum of a geometric series. Applications concern interest rates of loans and deposits as well as the calculation of a loan installment.

5. The notion of a function; properties of functions such as: the continuity, the convexity, the concept of a monotone function of a real single variable; basic properties of limits, examples, improper limits, one-sided limits; the limit of a function at a point and at infinity, checking the continuity of functions and the Weierstrass theorem.

6. The notion of a derivative of a function; computation of a derivative; the chain rule for composite functions. Introduction to the calculus of one variable and optimization.

7. The indefinite integral: the method of integration by parts and by a substitution; the area beneath the graph of a curve; The definite integral and the fundamental theorem of calculus

8. Functions of several variables: the concept of a function of several variables, the graph of a function of two variables; calculating partial derivatives, the gradient of a function; determining local extrema of a function of several variables.

9. A brief introduction to some concepts occuring in statistics and statistical inference as an application of the mathematical theory discussed during the semester.