151-0342/03 – Mathematics G (Mat G)

The student will be able ... • to interpret correctly the concept of the real function (one variable), • to find the domain of real functions of one real variable (by means of solving systems of non-linear inequations), • to characterize the basic properties of continuous functions, • to explain the behavior of certain discontinuous functions, • to compute and to interpret correctly the concept of limits of functions, • to define and compute the derivative of a function, • to interpret graphically the value of 1st and 2nd derivative of a function at a fixed point, • to find and to determine the local extrema, points of inflextion, asymptotes and to interpret these concepts graphical and from the practival point of view, • to control the basic rules for computing the antiderivative of a function, • to explain the concept of definite integral (Darboux approach), • to describe certain phenomenons with the help of the matrix algebra, • to solve the systems of linear equations by means of Gauß' elimination technique.

The course Mathematics G extends the basic concepts of mathematics and introduces the most important concepts of higher mathematics, i.e., the concept of limit of a function at a fixed point and the derivative of a function (as a special case of limit). Similarly, the course introduces the concept of integration (indefinite and definite integration). All this techniques have extensive applications in economic theories. Moreover, the course discuss also the solvability of systems of linear equations which forms the starting point for description of many problems from economic branche. Besides this facts, the student in the course should learn and fix the accuracy when arguing.

[1] Stewart J.S. Calculus - Concepts and Contexts. Cengage Learning, 2010. [2] Canuto C., Tabacco A. Mathematical Analysis I. Springer Verlag, 2008. [4] Luderer B., Nollau V., Vetters K. Mathematical Formulas for Economists. Springer Verlag, 3rd ed., 2007. [5] Tan T.S. Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011.

Requirements (100 points, minimum 51 points): Credit (45 points, minimal 23 points) 1. passing out the tests (at least 50 %), 2. sucesfull completion of all tasks until the end of the winter term (see the valid harmonogram). Exam (55 points, minimal 28 points) - combined 1. written part (max. 50 points, min. 26 points), 2. spoken part (max. 10 points, min. 5 points). Remark For passing out the spoken part of the exam, the absolute starting-popint is the precise accomplishment of all problems submitted by the teacher, especially theoretic problems and problems related to economic praxis. Submission of the problems, detailed instructions for elaborating and the relation of the submitted problems to PDF-versions of all lectures will be specified in the first seminar and also in the web-environment Moodle.