Calculus is the branch of mathematics that studies continuous change and is the principal precursor of modern mathematical analysis. It rests on two complementary divisions: differential calculus, which examines instantaneous rates of change and the slopes of curves, and integral calculus, which studies the accumulation of quantities and areas under curves. The two divisions are connected by the fundamental theorem of calculus, and both rest on the concept of a limit applied to infinite sequences and series.
Facts
Central QuestionCalculus studies continuous change: how the instantaneous rate at which a quantity changes (the derivative) and the total accumulation of a changing quantity (the integral) can each be defined rigorously and are related to one another through the fundamental theorem of calculus. 1 Key DebateIsaac Newton and Gottfried Wilhelm Leibniz each independently formulated infinitesimal calculus in the late 17th century, and when both published, a bitter priority dispute broke out over which mathematician, and therefore which country, deserved credit; it divided English-speaking mathematicians from continental European mathematicians for many years. 1 Classification
Pure or Applied Calculus
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1. Calculus (Wikipedia)
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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.
History section, Newton and Leibniz passage
When Newton and Leibniz first published their results, there was great controversy over which mathematician (and therefore which country) deserved credit.
Associated With: Analysis, Wikipedia lead paragraph, Calculus
Calculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis.
In Group: Calculus and Real Analysis, lead paragraph
Calculus is the branch of mathematics that studies continuous change, and is the principal precursor of modern mathematical analysis.
View the Source Oliver Heaviside (Wikipedia)
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independently developed vector calculus
View the Source Isaac Barrow (MacTutor)
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Isaac Barrow was an English mathematician who developed a method of determining tangents that closely approached the methods of calculus
View the Source Maria Gaetana Agnesi (Wikipedia)
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She is credited with writing the first book discussing both differential and integral calculus
View the Source Ramiro Rampinelli (Wikipedia)
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in the field of infinitesimal mathematics
View the Source Charles Babbage (Wikipedia)
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In 1816, Babbage, Herschel and Peacock published a translation from French of the lectures of Sylvestre Lacroix, which was then the state-of-the-art calculus textbook.
View the Source Grégoire de Saint-Vincent (MacTutor)
Includes: Grégoire de Saint-Vincent, Biography, LouvainQuote, Includes: Grégoire de Saint-Vincent, Biography, Louvain
developed methods which were important in setting the scene for the invention of the differential and integral calculus
View the Source Jyeṣṭhadeva (Wikipedia)
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Jyeṣṭhadeva (Malayalam: ജ്യേഷ്ഠദേവൻ; c. 1500, c. 1575) was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama (c. 1350, c. 1425).
View the Source Antoine de Laloubère (Wikipedia)
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With Cavalieri, Fermat, Vincentio, Kepler, Torricelli and Valerio, Lalouvere can be considered one of the forerunners of modern integral calculus.
View the Source Bernard Nieuwentyt (Wikipedia)
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In 1695 he was involved in a controversy over the foundations of infinitesimal calculus with Leibniz.
View the Source Michel Rolle (Wikipedia)
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Rolle is best known for Rolle's theorem in differential calculus.
View the Source Ajima Naonobu (Wikipedia)
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introducing calculus into Japanese mathematics
View the Source Evangelista Torricelli (Wikipedia)
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He is best known for his invention of the barometer, but is also known for his advances in optics and work on the method of indivisibles.
View the Source Gilles de Roberval (Wikipedia)
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of solids, which he accomplished, in some of the simpler cases, by an original method which he called the "Method of Indivisibles"; but he lost much of the credit of the discovery as he kept his method for his own use, while Bonaventura Cavalieri published
View the Source Guillaume de l'Hôpital (Wikipedia)
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This book was a first systematic exposition of differential calculus.
View the Source Takebe Kenkō (Wikipedia)
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Takebe played a critical role in the development of the Enri (円理, "circle principle") - a crude analogon to the western calculus.
View the Source Johannes Hudde (Wikipedia)
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And establishing two properties of polynomial roots known as Hudde's rules, that point toward algorithms of calculus.
View the Source Luigi Guido Grandi (Wikipedia)
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It was through his studies on this curve that Grandi helped introduce Leibniz' ideas on calculus to Italy.
View the Source Stefano degli Angeli (Wikipedia)
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From 1654 to 1667, he devoted himself to the study of geometry, continuing the research of Cavalieri and Evangelista Torricelli based on the method of Indivisibles.
View the Source Benjamin Robins (Wikipedia)
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directly stimulated the teaching of calculus in military academies
View the Source Bartholomew Lloyd (Wikipedia)
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introduction of the teaching of calculus
View the Source Hendrik van Heuraet (Wikipedia)
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He is noted as one of the founders of the integral, and author of Epistola de Transmutatione Curvarum Linearum in Rectus [On the Transformation of Curves into Straight Lines] (1659).
View the Source James Gregory (mathematician) (Wikipedia)
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his book Geometriae Pars Universalis (1668) Gregory gave both the first published statement and proof of the fundamental theorem of the calculus (stated from a geometric point of view, and only for a special class of the curves considered by later versions
View the Source John Craig (mathematician) (Wikipedia)
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A friend of Isaac Newton, he wrote several minor works about the new calculus.
View the Source Louis Carré (mathematician) (Wikipedia)
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He was the author of one of the first books on integral calculus.
View the Source William Neile (Wikipedia)
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geometry a basic concept from differential geometry, it represented a major advance in what would become infinitesimal
View the Source René-François de Sluse (Wikipedia)
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Sluse contributed to the development of calculus, focusing upon spirals, tangents, turning points and points of inflection.
View the Source Vittorio Francesco Stancari (Wikipedia)
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Stancari was awarded the chair of infinitesimal calculus in Bologna in 1708.
View the Source Humphry Ditton (Wikipedia)
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and rendering easier the writings of Galileo Galilei and Christiaan Huygens, and Principia of Newton; An Institution of Fluxions, containing the First Principles, Operations, and Applications of that admirable Method, as invented by Sir Isaac Newton
View the Source Esprit Pézenas (Wikipedia)
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He wrote on hydrography, the measurement of tonnage, differential calculus.
View the Source Michelangelo Ricci (Wikipedia)
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de maximis et minimis (1666) in which he studies the maxima of functions of the form xm(a−x)n and tangents to curves with equation ym=kxn, using methods that are an early form of
View the Source Charles Hayes (mathematician) (Wikipedia)
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In 1704, appeared his Treatise on Fluxions, or an Introduction to Mathematical Philosophy, London, the first English work explaining Isaac Newton's method of infinitesimals.
View the Source John Müller (Wikipedia)
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Mathematical Treatise: Containing a System of Conic-sections; with the doctrine of fluxions and fluents, applied to various subjects (1736) A Treatise Containing the Elementary Part of Fortification (1746) Elements of Mathematics (1748, also titled A System
View the Source Colin Maclaurin (Wikipedia)
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Maclaurin used Taylor series to characterize maxima, minima, and points of inflection for infinitely differentiable functions in his Treatise of Fluxions.
View the Source Chain rule (Wikipedia)
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In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions z and y
View the Source Gradient Theorem (Wikipedia)
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theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field
View the Source Squeeze Theorem (Wikipedia)
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In calculus, the squeeze theorem (also known as the sandwich theorem, the two policeman and a drunk theorem among other names) is
View the Source Differentiation Rules (Wikipedia)
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les for computing the derivative of a function in calculus.
View the Source Quotient Rule (Wikipedia)
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In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functio
View the Source Vector Field (Wikipedia)
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In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean spac
View the Source Limit of a Function (Wikipedia)
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e limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular
View the Source Second Derivative (Wikipedia)
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In calculus, the second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f.
View the Source Cavalieri's Quadrature Formula (Wikipedia)
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In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral ∫
View the Source Divergence (Wikipedia)
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In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that
View the Source Integral of the Secant Function (Wikipedia)
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In calculus, the integral of the secant function can be evaluated using a variety of methods and there are multiple ways of expres
View the Source Wikipedia: John Wallis
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who is given partial credit for the development of infinitesimal calculus
View the Source Wikipedia: Pietro Mengoli
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was a pivotal figure in the development of calculus
View the Source Wikipedia: George Gabriel Stokes
WikipediaIncludes: George Gabriel Stokes, Lead paragraphQuote, Includes: George Gabriel Stokes, Lead paragraph
As a mathematician, he popularised Stokes' theorem in vector calculus and contributed to the theory of asymptotic expansions.
View the Source Infinitesimal (Wikipedia)
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Infinitesimal numbers were introduced in the development of calculus, in which the derivative was first conceived as a ratio of two infinitesimal quantities.
View the Source Wolfram MathWorld: Dirichlet Function
Wolfram MathWorldIncludes: Dirichlet Function, Subject classificationsQuote, Includes: Dirichlet Function, Subject classifications
Calculus and Analysis Calculus
View the Source Wolfram MathWorld: Weierstrass Function
Wolfram MathWorldIncludes: Weierstrass Function, Subject classificationsQuote, Includes: Weierstrass Function, Subject classifications
Calculus and Analysis Calculus
View the Source Riemann-Stieltjes Integral (Wikipedia)
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In mathematics, the Riemann-Stieltjes integral is a generalization of the Riemann integral
View the Source Borwein Integral (Wikipedia)
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In mathematics, a Borwein integral is an integral whose unusual properties were
View the Source Symmetric Derivative (Wikipedia)
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In mathematics, the symmetric derivative is an operation generalizing the ordinary derivative.
View the Source Euler-Maclaurin Formula (Wikipedia)
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formula is a formula for the difference between an integral and a closely related sum. It can be used to
View the Source Bonaventura Cavalieri, Biography (MacTutor History of Mathematics)
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Bonaventura Cavalieri was an Italian mathematician who developed a method of indivisibles which became a factor in the development of the integral calculus.
View the Source Brook Taylor, Biography (MacTutor History of Mathematics)
Includes: Brook Taylor, SummaryQuote, Includes: Brook Taylor, Summary
Brook Taylor was an English mathematician who added to mathematics a new branch now called the 'calculus of finite differences', invented integration by parts, and discovered the celebrated formula known as Taylor's expansion.
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