The Newton Leibnaz

Controvercy The Fight Continues On.... By Simon Shum 12B Like Most Discoveries, Calculas was created by the long time effort of the collective group rather than a certain individual and instant epiphiny. Yet, there were two mathematician whose contribution towards calculus had outweighted all others Their names were, Sir Isaac Newton

and Gottfried Wilhelm Leibniz VS Background Calculas was catagorized as a more

general term of mathematic before

the discoveries were made by Newton and Leibniz During the periods of the Renaissance, mathmatician began to look towards contemporary thinkers during the time period. They developed techniques, formed ideologies and made variation towards the different branches of math Both Newton and Leibnaz were able to make major breakthroughs, but yet took two disticntive approach towards the the topic of Calculas. NEWTON'S cONTRIBUTION

towards CALCULuS His first actual contribution towards math was made the year 1664, as he expanded the binomiral theorem to include both fractional and negative exponents A series of discoveries were then made between the years of 1665 and 1666, which he stated to be the "the prime of my age for invention and mind mathematics and philosophy more than at any time since (1)." During the same year, he again advanced pertinency

of the Binomial theorem, by showing the potential

of the infinite series and using it as a term to

analyze the finite algebra. And it was during these two consecutive years that Newton brought out his theory of Fluxionary Calculus, which included the using of algerbraic expression to solidify the idea of an area under a curve that had a momentary rate of change. However, though Newton had calculated the area under a curve through antidifferentiation and had incorporated the fundemental theorem of Calculus , or now known as the second fundemental theorem of Calculus into his calculation, he was well aware of logical deficiency and the potential errors that his new theorem could cause. That is why in 1671, when he wrote the book of "Methodus Fluxionum et Serierum Infinitarum", where he used mathmatics to assimilate and back up certain theories of physic, while also redifined as previous calulation in the form of continuous motion, rather than momentary rate change. And instead of employing the use of infinitesimal on forming the explaination of the rate of change, Newton used fluxion that was represented by dotted letters, with quantity generated by the fluxion were called fluents. This idea was ultimately developed into the modern day derivates. Leibnaz Contribution towards Calculas Leibniz started his dicoveries on Calculus about the same time that Newton compiled his work on the Fluxionary Calculas. But when compared to, who started

his discoveries at age of 22 and 23, Leibnaz

began his mathmatical r4esearch

at an much intellectual age of 26. Though he was 3 years younger than newton, Leibniz had a wide variety of intrest before he was convinced and finalized his field of study towards Mathmatics. Like Newton, Leibniz also saw tangent as a ratio but did not use it as a defining property for his Calculas, and while Newton tried to avoid the use infinitesimals in prorving his theories, Leiniz on the other hand made infinitesimals the foundation for his calculas Leibnaz is most important legacy, would probably his invention of connotation, which proved to be important in the later development of Calculas, his creation include d (dx and dy) and (∫ ) are still used today. The product rule of differential calculation, and the theorem that explains to us the way of differentiation under a integral are named after his name. THE controvercy Though both of these mathmatician are now both given credit for their contribution in calculus, a long term debate did spark in the later years of Leibnaz' 's life over the question on who had came first in the invention of calculus? As an reowned mathmatician and an equally established author of many great works, Leibnaz had published his research on Calculus well before Newton did. Yet evidence show that Newton had dicovered his theories of Fluxionary Calculas 6 years before Leibnaz's , and was the first mathematician in Europe that make a clear statment on the fundemental theorem of Calculus. Rising speculations of the idea that Leibniz has based his exploration of Calculus on Newton's work rised even higher when many heard rumors about the idea that Leibniz had read Newton's unpublished paper of his discoveries on Calculus and was able to gain insights from the frequent conversation and letters between the two, as they were close friends. This, inevitably lead the people to believe that Leibniz had plagirized his theories from Newton's Discovery. In 1715, the Royal Acadamy establish the verdict of giving Newton the full credit for his discoveries on Calculus. On the hand, the verdict also charged Leibniz for plagiarizing Newton's work of Calculus. However, it was later discovered that Leibiniz work of Calculus did not copy Newton's in the first place. The fact that Leibniz had showed his intepretation and findings of Calculus in his letters to Newton, based on his own thoughts and belief and did not show any glimpse of Newton's ideologies, proved his innocence. But it was not until his death, that the false accusation and rumours had been calrified for his justification. Though it was arguable that whether Leibniz did actually gain any insights from Newton's papers, it is generally believed that Leibiniz had already formulated his theories of Caculus before they started to exchange ideas with one another. Calculus has sure came a long way ever since Newton's and Leibniz discoveries, and ever since their death, mthmaticians from around the world had also made their contribution towards this branch of mathematics. When compared with neither Leibniz's or Newton's work on calculus, one could easily infer that the modern day calculus tends to be much more systematic and explanatory than their original ideas, as many of the intepretation back then was very conceptual and lacked of logical proof. Also, some would see that their slight variation are also made on the logical base of our modern day calculus , which is because of the progression of ideologies through time has caused people to think adversly than our ancestors 300 years ago. good bye a f(t)dt = See You Next Time Question: When X equals GOOD BYE, WHEN DOES THE INTEGRAL OF FX EQUALS Work Cited http://www-history.mcs.st-and.ac.uk/HistTopics/The_rise_of_calculus.html

http://www.jimloy.com/calc/newtleib.htm

http://www.angelfire.com/md/byme/mathsample.html

http://en.wikipedia.org/wiki/Leibniz_and_Newton_calculus_controversy

http://shafali.files.wordpress.com/2010/05/caricature_cartoon_scientist_isaac_newton_apple_breakfast_in_heaven.jpg

http://en.wikipedia.org/wiki/Gottfried_Leibniz

http://en.wikipedia.org/wiki/History_of_calculus#Newton

http://www.sosmath.com/calculus/diff/der00/der00.html

http://www-history.mcs.st-and.ac.uk/HistTopics/The_rise_of_calculus.html

http://encyclozine.com/History/Biography/Newton/

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# Copy of The Real Inventor of Calculas

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