The Historical Development of the Calculus

by Charles Henry Edwards

Book Overview

This is a lucid account of the highlights in the historical development of the calculus from ancient to modern times - from the beginnings of geometry in antiquity to the nonstandard analysis of the... This description may be from another edition of this product.

• Format: Hardcover
• Language: English
• ISBN: 0387904360
• ISBN13: 9780387904368
• Release Date: January 1982
• Publisher: Springer
• Length: 368 Pages
• Weight: 1.55 lbs.

Customer Reviews

Useful resource, but dry and incomplete

The historical path is often more sensible than modern textbooks, as we see here in numerous cases: the logarithm should be understood as the area under the hyperbola y=1/x, Taylor series should be understood in terms of the Gregory-Newton interpolation formula, etc. But if there is one lesson history should teach calculus textbook authors it is this: power series. Power series were always indispensable and inseparable from the calculus at every stage of the development. Modern authors shoot themselves (and their students) in the foot by postponing power series as far as possible. Euler, in his Introductio, beautifully derives the derivatives of the elementary functions by power series methods, which is neat and systematic and makes use of concepts of great power and scope. By contrast, modern authors, suffering from rigour hiccups, insists that these derivatives must be deduced from "the definition" of the derivative, using horrendously ad hoc limit-manipulation tricks. This book is useful and certainly much better than Boyer's awful book, but it is still very far from being a satisfactory history of the calculus. In particular there is no physics, which is of course utterly absurd if it is to be a true history of the calculus. Also, it treats only the very basics of the calculus, essentially ignoring differential equations, several variables, the calculus of variations, etc.