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Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes given as An approach using infinitesimals .
Howard Jerome Keisler (born 3 December 1936) is an American mathematician, currently professor emeritus at University of Wisconsin–Madison. His research has included model theory and non-standard analysis .
Elementary calculus may refer to: The elementary aspects of differential and integral calculus ; Elementary Calculus: An Infinitesimal Approach , a textbook by Jerome Keisler.
As an application to mathematical education, H. Jerome Keisler wrote Elementary Calculus: An Infinitesimal Approach. [10] Covering nonstandard calculus , it develops differential and integral calculus using the hyperreal numbers, which include infinitesimal elements.
Howard Jerome Keisler: Elementary Calculus: An Infinitesimal Approach. First edition 1976; 2nd edition 1986. First edition 1976; 2nd edition 1986. This book is now out of print.
There was the nonstandard analysis movement for teaching elementary calculus. Its stock rose a bit before the movement collapsed from inner complexity and scant necessity. Nonstandard calculus in the classroom has been analysed in the study by K. Sullivan of schools in the Chicago area, as reflected in secondary literature at Influence of ...
Crowell, Brief Calculus. A text using infinitesimals. Hermoso, Nonstandard Analysis and the Hyperreals. A gentle introduction. Keisler, Elementary Calculus: An Approach Using Infinitesimals. Includes an axiomatic treatment of the hyperreals, and is freely available under a Creative Commons license
Keisler's Elementary Calculus: An Infinitesimal Approach defines continuity on page 125 in terms of infinitesimals, to the exclusion of epsilon, delta methods. The derivative is defined on page 45 using infinitesimals rather than an epsilon-delta approach.
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