Read Online The Historical Development of the Calculus Springer Study Edition CHJr Edwards 9780387943138 Books
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The calculus has served for three centuries as the principal quantitative language of Western science. In the course of its genesis and evolution some of the most fundamental problems of mathematics were first con fronted and, through the persistent labors of successive generations, finally resolved. Therefore, the historical development of the calculus holds a special interest for anyone who appreciates the value of a historical perspective in teaching, learning, and enjoying mathematics and its ap plications. My goal in writing this book was to present an account of this development that is accessible, not solely to students of the history of mathematics, but to the wider mathematical community for which my exposition is more specifically intended, including those who study, teach, and use calculus. The scope of this account can be delineated partly by comparison with previous works in the same general area. M. E. Baron's The Origins of the Infinitesimal Calculus (1969) provides an informative and reliable treat ment of the precalculus period up to, but not including (in any detail), the time of Newton and Leibniz, just when the interest and pace of the story begin to quicken and intensify. C. B. Boyer's well-known book (1949, 1959 reprint) met well the goals its author set for it, but it was more ap propriately titled in its original edition-The Concepts of the Calculus than in its reprinting.
Read Online The Historical Development of the Calculus Springer Study Edition CHJr Edwards 9780387943138 Books
"A forgotten masterpiece, suitable for advanced high school math students as well as undergrad college level study. Edwards' work does a more thorough job of explaining how math was discovered than any other math history book I have in my collection - and I have more than 500 works on mathematics in my library."
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The Historical Development of the Calculus Springer Study Edition CHJr Edwards 9780387943138 Books Reviews :
The Historical Development of the Calculus Springer Study Edition CHJr Edwards 9780387943138 Books Reviews
- A forgotten masterpiece, suitable for advanced high school math students as well as undergrad college level study. Edwards' work does a more thorough job of explaining how math was discovered than any other math history book I have in my collection - and I have more than 500 works on mathematics in my library.
- 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.
