USING INTEGRAL CALCULUS TO DEFINE SOME ELEMENTARY FUNCTIONS AS A NEW WAY TO TEACH SOME PARTS OF CALCULUS

In the contribution we define some basic elementary functions and derive their properties using integral calculus of a real function of one real variable. In doing so we assume that students have been acquainted with fundamentals of differential and integral calculus only, hence the introducing of some elementary functions arises directly of this assumption. Such a concept of teaching and studying elementary functions could be more attractive for students than usual ways of teaching them. This way of teaching calculus could be realized e. g. at secondary schools with groups of students talented in mathematics (if they have optional seminars on mathematics) or at the first year of university study programmes of various types during courses on calculus. Another possibility of teaching the calculus in such a way could reach good results when it would be applied at teacher training study programmes, so that the future teachers at secondary schools could obtain new skills to form their students in mathematical reasoning. We will point out also connections with some special functions defined by integrals that are often used in advanced mathematics and its applications.

Acknowledgement: This work has been supported by the Slovak grant agency KEGA under the grant No. 057ŽU - 4/2012.