THE FORMATION OF DIFFERENTIAL AND INTEGRAL CALCULUS BASED ON THE WORKS OF NEWTON AND LEIBNIZ

This article examines the historical and mathematical formation of differential and integral calculus on the basis of the scientific works of Isaac Newton and Gottfried Wilhelm Leibniz. The study analyzes the idea of infinitesimals, the problems of tangents and quadratures, the need to express motion and rates of change mathematically, Newton’s method of fluxions, and Leibniz’s symbolic system of differentials and integrals. It is argued that calculus did not emerge suddenly, but was the logical continuation of earlier mathematical ideas developed by Cavalieri, Fermat, Descartes, Barrow, Wallis, and other scholars. Newton interpreted calculus mainly through mechanical motion and time-dependent quantities, whereas Leibniz transformed it into a general symbolic and algorithmic method. The article also discusses the Newton–Leibniz priority dispute, the differences between their approaches, and the methodological importance of studying this historical process in modern higher mathematics education. The practical section contains two solved examples illustrating differentiation and integration in the context of the historical development of calculus.