Calculus

:For other uses of the term calculus see calculus (disambiguation)

History

Main article: History of calculus

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Though the origins of integral calculus are generally regarded as going back no farther than to the time of the ancient Greeks, circa 200 B.C., there is some evidence that the ancient Egyptians may have had some hint of the idea at a much earlier date. (See Moscow Mathematical Papyrus.) The Hellenic mathematician Eudoxus is generally credited with the method of exhaustion, which made it possible to compute the area of regions and the volume of solids. Archimedes developed this method further, while also inventing heuristic methods which resemble modern day concepts in calculus. Of all the mathematicians of the ancient world, he was the closest to discovering calculus, but he never made the breakthrough, and after him study of calculus did not advance appreciably for more than a thousand years.

Related Topics:
Ancient Greeks - Ancient Egyptians - Moscow Mathematical Papyrus - Hellenic - Eudoxus - Method of exhaustion - Archimedes

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An Indian mathematician, Bhaskara (1114-1185), developed a number of ideas that can now be seen to be forerunners of calculus and gave the basic idea of what is now known as "Rolle's theorem". He was the first to conceive the idea of differential calculus. The 14th century Indian mathematician Madhava, along with other mathematicians of the Kerala school studied infinite series, convergence, differentiation, and iterative methods for solution of non-linear equations. Jyestadeva of the Kerala school wrote the first calculus text, the Yuktibhasa, which explores methods and ideas of calculus that were only repeated in seventeenth century Europe.

Related Topics:
Indian mathematician - Bhaskara - Rolle's theorem - Indian mathematician - Madhava - Kerala school

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Leibniz and Newton are usually designated the inventors of calculus. The ideas of differentiation, integration, and even of the Fundamental Theorem were known earlier, by Wallis, Barrow, and other mathematicians. The main contribution for which Leibniz and Newton are honored is putting these pieces together into a coherent whole. Leibniz developed much of the notation used in calculus today.

Related Topics:
Leibniz - Newton - Wallis - Barrow

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There has been considerable debate about whether Newton or Leibniz was first to come up with the important concepts of calculus. The truth of the matter is that the ideas of calculus were a part of the mathematical knowledge of their day, and they independently put those pieces together in different but coherent ways. The mathematical proofs of much of what they did came later, with Cauchy and others. Leibniz' greatest contribution to calculus was his notation; he often spent days trying to come up with the appropriate symbol to represent a mathematical idea. This controversy between Leibniz and Newton was unfortunate in that it divided English-speaking mathematicians from those in Europe for many years, setting back British analysis (i.e. calculus-based mathematics) for a very long time. Newton's terminology and notation was clearly less flexible than that of Leibniz, yet it was retained in British usage until the early 19th century, when the work of the Analytical Society successfully saw the introduction of Leibniz's notation in Great Britain. It is now thought that Newton had discovered several ideas related to calculus earlier than Leibniz had; however, Leibniz was the first to publish. Today, both Leibniz and Newton are considered to have discovered calculus independently.

Related Topics:
Cauchy - Notation - Analytical Society

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Lesser credit for ideas that led to the development of calculus is given to Descartes, Barrow, de Fermat, Huygens, and Wallis. A Japanese mathematician, Kowa Seki, lived at the same time as Leibniz and Newton and independently elaborated some of the fundamental principles of integral calculus. http://www2.gol.com/users/coynerhm/0598rothman.html

Related Topics:
Descartes - Barrow - De Fermat - Huygens - Wallis - Kowa Seki

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