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The following other wikis use this file: Usage on en.wikisource.org Wikisource:Community collaboration/Monthly Challenge/August 2022; Index:Calculus Made Easy.pdf
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.
Topics on Calculus at PlanetMath. Calculus Made Easy (1914) by Silvanus P. Thompson Full text in PDF; Calculus on In Our Time at the BBC; Calculus.org: The Calculus page at University of California, Davis – contains resources and links to other sites; Earliest Known Uses of Some of the Words of Mathematics: Calculus & Analysis
Topics on Calculus at PlanetMath. Calculus Made Easy (1914) by Silvanus P. Thompson Full text in PDF; Calculus.org: The Calculus page at University of California, Davis – contains resources and links to other sites; COW: Calculus on the Web at Temple University - contains resources ranging from pre-calculus and associated algebra
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 ...
Calculus textbooks based on infinitesimals include the classic Calculus Made Easy by Silvanus P. Thompson (bearing the motto "What one fool can do another can" [15]) and the German text Mathematik fur Mittlere Technische Fachschulen der Maschinenindustrie by R. Neuendorff. [16]
This short text is designed more for self-study or review than for classroom use. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals
In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, Green’s theorem and Stokes' theorem are the cases of a surface in or , and the divergence theorem is the case of a volume in . [2] Hence, the theorem is sometimes referred to as the fundamental theorem of multivariate calculus.
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