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Calculus 𓆩⚪𓆪｜Definition｜1st｜20251119205401-00-⌔

Calculus - Wikipedia

Calculus

Calculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis. Originally called infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus studies instantaneous rates of change and slopes of curves; integral calculus studies accumulation of quantities and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. Calculus uses convergence of infinite sequences and infinite series to a well-defined mathematical limit.1

Calculus is the “mathematical backbone” for solving problems in which variable quantities change with time or another reference value.2 It has also been called “the basic instrument of physical science”.3

In the late 17th century, Isaac Newton and Gottfried Wilhelm Leibniz each independently formulated infinitesimal calculus.45 Later work, including the formalization of the concept of limits, put calculus on a more solid conceptual footing. The concepts and techniques of calculus have broad applications in science, engineering, and other branches of mathematics.67

Printed 2026-06-28.

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Footnotes

  1. DeBaggis, Henry F.; Miller, Kenneth S. (1966). Foundations of the Calculus. Philadelphia: Saunders. OCLC 527896. ↩

  2. Fox, Huw; Bolton, Bill (2002), “Calculus”, Mathematics for Engineers and Technologists, Elsevier, pp. 99–158, doi:10.1016/b978-075065544-6/50005-9, ISBN 978-0-7506-5544-6, retrieved 24 November 2024 ↩

  3. Westfall, Richard S. (1981). “The Career of Isaac Newton: A Scientific Life in the Seventeenth Century”. The American Scholar. 50 (3): 341–53. ISSN 0003-0937. JSTOR 41210741. ↩

  4. Boyer, Carl B. (1959). The History of the Calculus and its Conceptual Development. New York: Dover. pp. 47, 187–88. OCLC 643872. ↩

  5. Bardi, Jason Socrates (2006). The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time. New York: Thunder’s Mouth Press. pp. v–vii. ISBN 1-56025-992-2. ↩

  6. Hoffmann, Laurence D.; Bradley, Gerald L. (2004). Calculus for Business, Economics, and the Social and Life Sciences (8th ed.). Boston: McGraw Hill. ISBN 0-07-242432-X. ↩

  7. Gibson, Jason (18 March 2017). “How Isaac Newton Changed the World with the Invention of Calculus”. Math Tutor DVD. Retrieved 23 December 2025. ↩

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