ADVANTAGES OF TEACHING MATHEMATICAL ANALYSIS THROUGH THE THEORY OF ELEMENTARY FUNCTIONS

Abstract

This research substantiates a new didactic approach to teaching differential and integral calculus in secondary schools by focusing exclusively on the theory of elementary functions. The approach assumes the continuity of elementary functions as an intuitive fact and integrates this assumption into the process of learning limits, derivatives, and integrals. The method eliminates redundant theoretical barriers, reduces abstraction, and establishes a logical transition from school-level mathematics to higher education. It is a practical realization of Academician A.N. Kolmogorov’s idea that the theory of continuous functions should be taught at school, while the general theory of functions should be studied in universities.