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Calculus: Role of Newton

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Brittany Schepak

on 14 February 2013

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Transcript of Calculus: Role of Newton

Calculus: Ch. 5 The Real Role of Newton in the Development of Calculus By: Brittany Schepak The first ideas of Calculus didn't come from Newton or Leibniz. The first ideas came from a group of Greek Mathematicians, one of whom, Pierre de Fermat, influenced Newton's thinking when he explored Calculus Isaac
Newton Pierre de Fermat Sources http://en.wikipedia.org/wiki/History_of_calculus
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html Newton became interested in Calculus because his work with Geometry and Physics led him to explore some of the elements of calculus to explain the scientific descriptions of magnitude and motion. Calculus was first hinted at in 450 BC by Zeno of Elea, but was really starting to form in the 17th century with several Greek mathematicians Newton originally looked in Calculus problems for his own use, using symbols and notation that he could follow and didn't bother putting it into an exact format.
*Leibniz was the exact opposite and made sure he put thought into his notation so most of the notation we see today is Leibniz's. A Brief History of Calculus What Newton Contributed He first discovered how to find the area under a curve by using infinitesimals (or numbers that are so close to zero that it really can't be distinguished from zero. Ex.: .0000001) He used a unique method with finding the area of triangles under the curve to find the area. Diagram of how Newton discovered area under a curve This discovery led to him incorporating the first draft of the Fundamental Theorem of Calculus into his calculations. At this point in time, he was also calculating areas using antiderivatives. Newton tended to focus his finding in Calculus on how it related to motion, rates of change, and variables of change, while Leibniz focused on variables ranging over inifinitely close values. Like Leibniz, Newton didn't focus on functions, but focused on graphs and provided part of the foundation for calculus today Gottfried Leibniz Later on, mathematicians like Lord Bishop Berkeley, Cauchy, Weierstrass, and Riemann perfected calculus and put the formulas of derivatives and integrals in terms of limits, instead of infinitesimals.
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