THE FORMATION OF DIFFERENTIAL AND INTEGRAL CALCULUS BASED ON THE WORKS OF NEWTON AND LEIBNIZ
Keywords:
differential calculus, integral calculus, Newton, Leibniz, fluxion, differential, infinitesimals, quadrature, tangent, history of mathematics.Abstract
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.
References
Zeuthen, H. G. History of Mathematics in the Sixteenth and Seventeenth Centuries. Translated from German by P. Novikov; edited, annotated, and introduced by M. Vygodsky. Moscow–Leningrad: ONTI, 1938.
Newton, I. Philosophiae Naturalis Principia Mathematica. Londini: Jussu Societatis Regiae ac Typis Josephi Streater, 1687.
Newton, I. The Method of Fluxions and Infinite Series; with its Application to the Geometry of Curve-lines. Translated from the Latin by John Colson. London: Henry Woodfall; sold by John Nourse, 1736.
Leibniz, G. W. Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus. Acta Eruditorum. Lipsiae, October 1684, pp. 467–473.
Leibniz, G. W. De geometria recondita et analysi indivisibilium atque infinitorum. Acta Eruditorum. Lipsiae, June 1686, pp. 292–300.
Struik, D. J. A Source Book in Mathematics, 1200–1800. Princeton: Princeton University Press, 1986.
Boyer, C. B. The History of the Calculus and Its Conceptual Development. New York: Dover Publications, 1959.
Edwards, C. H. The Historical Development of the Calculus. New York: Springer-Verlag, 1979.
Katz, V. J. A History of Mathematics: An Introduction. 3rd ed. Boston: Addison-Wesley, 2009.
Hall, A. R. Philosophers at War: The Quarrel between Newton and Leibniz. Cambridge: Cambridge University Press, 1980.
Azerbaijan
Türkiye
Uzbekistan
Kazakhstan
Turkmenistan
Kyrgyzstan
Republic of Korea
Japan
India
United States of America
Kosovo