elementary calculus an approach using infinitesimals

#Elementary calculus an approach using infinitesimals full#

Keisler, Elementary Calculus : An Approach Using Infinitesimals, Prindle. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results. when x goes to zero in the infinitesimal approach, the derivative is. Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. 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. It can be used as a quick introduction to the infinitesimal approach to calculus for mathematicians, as background material for instructors, or as a text for an undergraduate seminar. The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. This monograph is a companion to the online edition of my textbook Elementary Calculus: An Approach Using Infinitesimals''.

pdf) files: Foundations of Infinitesimal Calculus on my web site and the Epilog to Keislers text, Elementary Calculus: An Approach Using Infinitesimals on his web site. For a more traditional text designed for classroom use, see Fundamentals of Calculus (). The following presentation of Keislers foundations for Robinsons Theory of Infinitesimals is explained in more detail in either of the (free. The book is available freely online and is currently published by Dover. The subtitle alludes to the infinitesimal numbers of the hyperreal number system of Abraham Robinson and is sometimes given as An approach using infinitesimals.

#Elementary calculus an approach using infinitesimals full#

This short text is designed more for self-study or review than for classroom use full solutions are given for nearly all the end-of-chapter problems. Template:Italic title Elementary Calculus: An Infinitesimal approach is a textbook by H.