Calculus

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

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Calculus is one of the most important breakthroughs in modern mathematics, answering questions that had puzzled mathematicians, scientists, and philosophers for more than two thousand years. In particular, calculus gave a clear and precise definition of infinity, both in the case of the infinitely large and the infinitely small. It provided an answer to Zeno's paradoxes and gave the first clear definition of what Aristotle called "the quality of motion".

Related Topics:
Mathematics - Scientist - Philosopher - Definition - Infinity - Zeno's paradox - Aristotle

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Calculus was not discovered all at once. In the ancient world, Eudoxus and Archimedes proposed mathematical ideas that can now be seen as similar to calculus. In Twelfth Century India, Bhaskara conceived of differential calculus and two centuries later, Madhava and the Kerala school studied infinite series, convergence, differentiation and other concepts of calculus. In the 17th century, Kowa Seki in Japan elaborated some of the fundamental principles of integral calculus. At roughly the same time, in Europe, Wallis and Barrow proposed ideas that would now be considered integrals, derivatives, and the fundamental theorem of calculus. But it was Newton and Leibniz who brought all these ideas together, and they are usually credited with the independent and nearly simultaneous creation of calculus. Even so, it was generations after Newton and Leibniz that Cauchy and other mathematicians finally put calculus on a rigorous basis, with the definition of the limit.

Related Topics:
Eudoxus - Archimedes - Twelfth Century - India - Bhaskara - Differential calculus - Madhava - Kerala - Infinite series - Convergence - Differentiation - 17th century - Kowa Seki - Japan - Integral calculus - Europe - Wallis - Barrow - Integral - Derivative - Fundamental theorem of calculus - Newton - Leibniz - Cauchy - Limit

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From a mathematical standpoint, calculus gives the definitions and properties of three linear operators, the limit, the derivative, and the integral. All of these depend on the definition of the limit. Roughly speaking, the limit allows us to control an otherwise uncontrollable output, the derivative is the slope of a graph, and the integral is the area under a curve. In scientific applications, the derivative is often used to find the velocity given the displacement, and the integral is often used to find the displacement given the velocity. The fundamental theorem of calculus roughly states that the derivative and the integral are inverse operators.

Related Topics:
Linear operators - Limit - Derivative - Integral - Slope - Graph - Area - Velocity - Fundamental theorem of calculus

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Today, calculus is used in every branch of science and engineering, in business, in medicine, and in virtually every human endeavor where the goal is an optimum solution to a problem that can be given in mathematical form.

Related Topics:
Science - Engineering - Business - Medicine - Optimum

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