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This file has been identified as being free of known restrictions under copyright law, including all related and neighboring rights. ... Calculus Made Easy.pdf/270 ...
Calculus Made Easy ignores the use of limits with its epsilon-delta definition, replacing it with a method of approximating (to arbitrary precision) directly to the correct answer in the infinitesimal spirit of Leibniz, now formally justified in modern nonstandard analysis and smooth infinitesimal analysis.
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
Willis Eugene Lamb Jr. (/ l æ m /; July 12, 1913 – May 15, 2008) was an American physicist who won the Nobel Prize in Physics in 1955 "for his discoveries concerning the fine structure of the hydrogen spectrum."
Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals. Based on the ideas of F. W. Lawvere and employing the methods of category theory, it views all functions as being continuous and incapable of being expressed in terms of discrete entities. As a theory, it is a subset of synthetic differential ...
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Recently, Katz & Katz [8] give a positive account of a calculus course based on Keisler's book. O'Donovan also described his experience teaching calculus using infinitesimals. His initial point of view was positive, [9] but later he found pedagogical difficulties with the approach to nonstandard calculus taken by this text and others. [10]
Early editions of Silvanus P. Thompson's Calculus Made Easy use the older term. [3] In his 1998 update of this text, Martin Gardner lets the first use of "differential coefficient" stand, along with Thompson's criticism of the term as a needlessly obscure phrase that should not intimidate students, and substitutes "derivative" for the remainder ...
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