roots of calculas
Anwar Shamim Wazir
MS Advance Computational Science| Deep Learning for Physics, CV & Time Series , RL, High Performance Computing, Scientific Computing ( C++) & Edge Computing |
THE ROOTS OF CALCULUS
Today’s exciting applications of calculus have roots that can be traced to the work of the Greek mathematician Archimedes, but the actual discovery of the fundamental principles of calculus was made independently by Isaac Newton (English) and Gottfried Leibniz (German) in the late seventeenth century. The work of Newton and Leibniz was motivated by four major classes of scienti?c and mathematical problems of the time:
? Find the tangent line to a general curve at a given point.
? Find the area of a general region, the length of a general curve, and the volume of a general solid.
? Find the maximum or minimum value of a quantity—for example, the maximum and minimum distances of a planet from the Sun, or the maximum range attainable for a projectile by varying its angle of ?re.
? Given a formula for the distance traveled by a body in any speci?ed amount of time,?nd the velocity and acceleration of the body at any instant. Conversely,given a formula that
speci?es the acceleration of velocity at any instant, ?nd the distance traveled by the body in a speci?ed period of time.
Newton and Leibniz found a fundamental relationship between the problem of ?nding a tangent line to a curve and the problem of determining the area of a region. Their realization of this connection is considered to be the “discovery of calculus.” Though Newton saw how these two problems are related ten years before Leibniz did, Leibniz published his work twenty years before Newton. This situation led to a stormy debat eover who was the rightful discoverer of calculus. The debate engulfed Europe for half a century, with the scientists of the European continent supporting Leibniz and those from England supporting Newton. The con?ict was extremely unfortunate because Newton’s inferior notation badly hampered scienti?c development in England, and the Continent in turn lost the bene?t of Newton’s discoveries in astronomy and physics for nearly ?fty years. In spite of it all, Newton and Leibniz were sincere admirers of each other’s work.