DEFINITION OF THE ELEMENTARY FUNCTIONS ON THE PRINCIPLE OF THE MATHEMATICAL ANALYSIS

Abstract

The elementary functions occupy the special place in school maths and at the study of mathematical analysis in universities .Usually the study of elementary functions begins with the definition of basic elementary functions. Elementary methods are used, without regard to difficulties and imperfections of similar methods. Often rely on intuition, although, it will be desirable to give definition and studies of properties of functions at more logical level. This is old problem, but it is also actual today. The mathematicians were interested in the problem of introduction the definition of the power operations and the logarithms since the sixteenth century, but a main contribution to the decision of this problem belongs to Euler, his book "Introductio in analisin infinitorum - Lausanannae, 1748" became basic level in development of mathematical analysis and by inalienable part in educational literature. Later to the questions of methodology of introduction of definitions basic the elementary functions an attention has been given a number of well-known mathematicians such as F.Kiein, N.Bourbaki, R.Kurant et al. Basic idea: of using the methods of mathematical analysis for the construction of more complete theory. But this suggestion wasn’t very successful in methodology of study of the elementary functions not only at school but also at higher educational establishments. There are many different ways of studying basic elementary functions (logarithmic, exponential, sine, cosine) with the using of differential, integral calculus and the theory of power series are shown in this article.