History of calculus

History of calculus is 100% European... ..integral.. derivatives... infinite power series....differential equations.. Indians will answer that is not true.. that in Nalanda universities they had discovered calculus long before European ect ect .. but they can't show ANY WRITTEN RECORD or PROOF about their claims..and they can't provide proof of the existence of Nalanda university during middle age.....

N° 4 countries were involved in the development of calculus plus ancient Greece..

Italy
France
England
Germany..

Among other 'integrations' by Archimedes were the volume and surface area of a sphere, the volume and area of a cone, the surface area of an ellipse, the volume of any segment of a paraboloid of revolution and a segment of an hyperboloid of revolution.

No further progress was made until the 16th Century when mechanics began to drive mathematicians to examine problems such as centres of gravity. Luca Valerio (1552-1618) published De quadratura parabolae Ⓣ in Rome (1606) which continued the Greek methods of attacking these type of area problems. Kepler, in his work on planetary motion, had to find the area of sectors of an ellipse. His method consisted of thinking of areas as sums of lines, another crude form of integration, but Kepler had little time for Greek rigour and was rather lucky to obtain the correct answer after making two cancelling errors in this work.

Three mathematicians, born within three years of each other, were the next to make major contributions. They were Fermat, Roberval and Cavalieri. Cavalieri was led to his 'method of indivisibles' by Kepler's attempts at integration. He was not rigorous in his approach and it is hard to see clearly how he thought about his method. It appears that Cavalieri thought of an area as being made up of components which were lines and then summed his infinite number of 'indivisibles'. He showed, using these methods, that the integral of xnx^{n}xn from 0 to aaa was an+1/(n+1)a^{n+1}/(n + 1)a n+1/(n+1) by showing the result for a number of values of nnn and inferring the general result.