The Calculus Conflict By Abdul Rahman Zindani A

The Calculus Conflict By: Abdul Rahman Zindani

A History of Calculus › › › › › 1666 Newton invents his system for calculus 1675: Leibniz invents infinitesimal (differential) calculus 1684: Leibniz publishes his system of calculus 1687: Newton publishes his findings on the geometric form of calculus in Principia 1696: L’Hopital publishes a text discussing Leibniz’s calculus and its similarity to Newton’s findings. 1704: Newton releases his fluxional notation for calculus in print 1711: The calculus controversy breaks out between mathematicians 1770: Lagrange notation for derivatives is published 1820 s: Leibniz’s calculus became accepted again in

GOTTFRIED WILHELM LEIBNIZ • 1646 -1716 • One of the three great 17 th Century rationalists along with Descartes and Spinoza • Member of the Royal Society of London • Pioneer of the use of the binary system • Revived the use of matrices to solve equations

SIR ISAAC NEWTON • 1643 -1727 • Physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian • Principia is considered one of the most influential books in the history of science • President of the Royal Society in London • Became the first scientist to ever be knighted in 1705

The Controversy LEIBNIZ CLAIMED THAT HIS WORKS DEVELOPED INDEPENDENTLY › Published a description of his work prior to Newton mass printing anything › His personal papers show development of ideas of calculus following a different path from Newton NEWTON CLAIMED THAT LEIBNIZ HAD PLAGIARIZED HIS WORK › Newton and Leibniz had exchanged papers and letters in 1677 that contained Newton’s calculus notations and fundamentals › Supported by the Royal Society of London – Newton was the president at the time

Controversy (cont. ) › Leibniz started from the development of integrals – Summations of infinite series › Newton began his work with derivatives › Both were aware of each others’ work since they had worked together on the power series › Copies of Newton’s early manuscripts were found while going through Leibniz’s manuscripts in 1849 – These manuscripts were most likely copied after Leibniz had already published his own works › The controversy caused English mathematicians to separate from other Europeans › It was finally accepted that both men had made their discoveries independently – English mathematicians acknowledged Leibniz’s works again – Leibniz had already been dead for over a century

Notations of Calculus LEIBNIZ NEWTON › ›

Benefits LEIBNIZ NEWTON › ›

Modern Calculus › Today’s calculus is most like that of Leibniz’s – In terms of notation and the logic behind solving calculus problems – In a way, Leibniz was the one that won › The product rule of derivatives is also known as Leibniz’s Rule › The Fundamental Theorem of Calculus is sometimes referred to as the Newton-Leibniz formula › The prime notation (f ’(x) and f ’’(x)) was later developed by Joseph Louise Lagrange

Examples LEIBNIZ NEWTON

Bibliography