Editing Calculus (section)

{{Short description|Branch of mathematics}}
{{About|the branch of mathematics}}
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{{Calculus}}
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'''Calculus''' is the [[mathematics|mathematical]] study of <!-- Please, do not link "continuous" or "change", they have the common-language meanings, and do not refer to any technical mathematical concept -->continuous change, in the same way that [[geometry]] is the study of shape, and [[algebra]] is the study of generalizations of [[arithmetic operations]].

Originally called '''infinitesimal calculus''' or "the calculus of [[infinitesimal]]s", it has two major branches, [[differential calculus]] and [[integral calculus]]. The former concerns instantaneous [[Rate of change (mathematics)|rates of change]], and the [[slope]]s of [[curve]]s, while the latter concerns accumulation of quantities, and [[area]]s under or between curves. These two branches are related to each other by the [[fundamental theorem of calculus]]. They make use of the fundamental notions of [[convergence (mathematics)|convergence]] of [[infinite sequence]]s and [[Series (mathematics)|infinite series]] to a well-defined [[limit (mathematics)|limit]].<ref>{{cite book |first1=Henry F. |last1=DeBaggis |first2=Kenneth S. |last2=Miller |title=Foundations of the Calculus |location=Philadelphia |publisher=Saunders |year=1966 |oclc=527896 }}</ref> It is the "mathematical backbone" for dealing with problems where variables change with time or another reference variable.<ref>{{Citation |last1=Fox |first1=Huw |title=Calculus |date=2002 |work=Mathematics for Engineers and Technologists |pages=99–158 |url=https://linkinghub.elsevier.com/retrieve/pii/B9780750655446500059 |access-date=2024-11-24 |publisher=Elsevier |language=en |doi=10.1016/b978-075065544-6/50005-9 |isbn=978-0-7506-5544-6 |last2=Bolton |first2=Bill}}</ref>

Infinitesimal calculus was formulated separately in the late 17th century by [[Isaac Newton]] and [[Gottfried Wilhelm Leibniz]].<ref>{{cite book |last=Boyer |first=Carl B. |author-link=Carl Benjamin Boyer |url=https://archive.org/details/the-history-of-the-calculus-carl-b.-boyer |title=The History of the Calculus and its Conceptual Development |publisher=Dover |year=1959 |location=New York |pages=47, 187–188 |oclc=643872 |url-access=registration}}</ref><ref>{{cite book |first=Jason Socrates |last=Bardi |title=The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time |location=New York |publisher=Thunder's Mouth Press |year=2006 |isbn=1-56025-706-7 }}</ref> Later work, including [[(ε, δ)-definition of limit|codifying the idea of limits]], put these developments on a more solid conceptual footing. The concepts and techniques found in calculus have diverse applications in [[science]], [[engineering]], and other branches of mathematics.<ref>{{cite book |last1=Hoffmann |first1=Laurence D. |last2=Bradley |first2=Gerald L. |title=Calculus for Business, Economics, and the Social and Life Sciences |location=Boston |publisher=McGraw Hill |year=2004 |edition=8th |isbn=0-07-242432-X }}</ref><ref>{{Cite web |last= |first= |date=2017-03-18 |title=How Isaac Newton Changed the World with the Invention of Calculus |url=https://www.mathtutordvd.com/public/How-Isaac-Newton-Changed-the-World-with-the-Invention-of-Calculus.cfm |access-date=2024-11-26 |website=www.mathtutordvd.com }}</ref>