Page 89 - AGRANI SAMKALP SILVER JUBILEE SOUVENIR

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To support his investigations in physics and geometry mathematicians have contributed to the continuing
Newton started working with calculus to employ it as the development of calculus. In 1680 Jacob Bernoulli not only
scientific description of the generation of motion and coined the term integral calculus but also developed
magnitudes. During his plague-induced isolation (1665-1666) differential equations and a method to solve it now called as
he recorded his first conception of fluxionary calculus in the separation of variables. In 1690, L'Hôpital's developed a
unpublished paper De Analysi per Aequationes Numero method for finding the limiting value of fractions of the type
Terminorum Infinitas in which he determined the area under 0/0 now called as L'Hospital's rule for finding limits. In same
a curve by first calculating a momentary rate of change and year, Michel Rolle in his paper Demonstration gave Mean
then extrapolating the total area. By considering a momentary Value Theorem for derivative. After this progress in Calculus,
increase at a point he developed an expression for the area Brooke Taylor developed Taylor's Series, Leonhard Euler
under a curve. In 1671, he compiled his work on fluxional invented the calculus of variations and formulated the Euler-
calculus in Methodus Fluxionum et Serierum Infinitarum, to Lagrange equation for reducing optimization problems,
give calculus a more rigorous explication and framework. In Joseph-Louis Lagrange invented the method of solving
this book he exploited instantaneous motion and differential equations known as variation of parameters and
infinitesimals informally. Joseph Fourier gave the representation of functions by
While Newton began development of his fluxional trigonometric (Fourier) series. Bernard Bolzano, Karl
calculus in 1665-1666 his findings did not become widely Weierstrass, Augustin-Louis Cauchy, Bernhard Riemann,
circulated until later. In the intervening years, Leibniz also George Cantor, Charles Hermite, Henri Poincaré, and Henri-
strove to create his calculus. Léon Lebesgue further contributed to calculus in their own
way.
An important point to note here is that the elementary
bases on which Newton and Leibniz created their calculus Now, one might wonder why Leibniz and Newton were
were different. For Newton, change was a variable quantity given the credit of inventing calculus, if they did not invent
over time and for Leibniz it was the difference ranging over derivatives, integration, Taylor series, or even the
a sequence of infinitely close values. They both were trying Fundamental Theorem of Calculus. The answer is that
to create a mathematical system to deal with variable Newton and Leibniz were the first who took all of the distinct
quantities, but they did not conceive of modern calculus. results and ideas and developed a reasonably systematic and
There was much debate over whether it was Newton or formal way to deal with infinitesimal and proved more
Leibniz who first “invented” calculus. This argument, the general results than anyone who had preceded them.
Leibniz and Newton calculus controversy, led to a rift in the Since, history has a tendency to attribute whole theories
European mathematical community lasting over a century. and results to single individual, so only few get credit of
Today, both Newton and Leibniz are given credit for whole of preceding results that made their accomplishments
independently developing the basics of calculus. However, possible.
it was Leibniz who gave the new discipline the name it is In Newton's own words, “If I have seen further, it is by
known by today: “calculus”. standing on the shoulders of giants.”
Since the time of Leibniz and Newton, many 

“A passion for calculus can unlock new worlds.”
-Isaac Newton

“An equation for me has no meaning, unless it expresses a thought of God.”
-Srinivasa Ramanujan

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