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AGRANI SAMKALP SILVER JUBILEE SOUVENIR

“Kerala school of mathematics” (a group of mathematicians of analysis of Descartes and Cavalieri. By integration, he
in southern part of India) expanded on Bhaskara's work and proved that the ratio of area enclosed between the curve y=x ,
m
further advanced the development of calculus in India. It is x-axis, and any ordinate x=h, to that of the parallelogram on
believed that Madhava (1340-1425) and the Kerala School the same base and of the same height is 1/(m+1), extending
mathematicians (including Parameshvara, Nilaknta, Cavalieri's quadrature formula.
Jyeshtadeva) developed initial theory of calculus before 14th A critical breakthrough occurred in November 1675,
century. Their main discovery was integral of x^n. when Gottfried Wilhelm Leibniz employed integral calculus
for the first time to find the area under the graph of a function
y = f(x). He denoted the infinitesimal increments of abscissas
and ordinates dx and dy, and introduced several notations
Pages from used to this day, for instance the integral sign ò, representing
Rigveda an elongated S, from the Latin word summa (sum/total), and
manuscript of the d used for differentials, from the Latin word differentia
mathematics in (difference/diversity/distinction).But Leibniz did not publish
Sanskrit on paper anything about his calculus until 1684.

The Arabs and Persians too made notable contributions
to the foundation of calculus a few centuries before
Madhavan. In his Al-Mu'adalat (Treatise on Equations),
Sharaf-al-Din-al-Tusi, a 12th century mathematician in
Middle east, found algebraic and numerical solutions of cubic
equations and was the first to discover the derivative of cubic
polynomials, which is an important result in differential
calculus.
Graphs referenced Problem formulated
In 1625, Grégorie de St Vincent developed a method of
and solved by
infinitesimals which he thought he could use to find in Leibniz' article Leibniz Calculus.
of 1684
quadrature of a circle. In Methodus ad disquirendam
maximam et minimam and in De tangentibus linearum In 1668, James Gregory published his book Geometriae
curvarum, Pierre de Fermat developed a method (adequality) Pars Universalis in which he gave both the first published
for determining maxima, minima, and tangents to various statement and proof of a rudimentary form of the fundamental
curves that was equivalent to differential calculus. In these theorem of the calculus which was strongly geometric in
works, Fermat obtained a technique for finding the centers character. Later, Isaac Barrow proved a more generalized
of gravity of various plane and solid figures, which led to his version of the theorem and such deserves credit as one of the
further work in quadrature. In his two treatises: Mirifici inventors of modern calculus. His student Isaac Newton
Logarithmorum Canonis Descriptio (Description of the (1642-1727) completed the development of the surrounding
Marvelous Canon of Logarithms), which was published in mathematical theory.
1614, John Napier gave an account of the nature of
logarithms. In 1627, Bonaventura Cavalieri developed a new
geometrical approach called the method of indivisibles which
is fundamental feature of integral calculus. He also proved Isaac Newton (1642-1727)
published Analysis per quantitatum
which is now known as Cavalieri's quadrature series, fluxiones ac differentias
formula.
in 1711.
In 1656 John Wallis published his most important work
Arithmetica Infinitorum, in which he extended the methods

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