Home » A Guide to Cauchys Calculus - A Translation and Analysis of Calcul Infinitesimal by Dennis M. Cates
A Guide to Cauchys Calculus - A Translation and Analysis of Calcul Infinitesimal Dennis M. Cates

A Guide to Cauchys Calculus - A Translation and Analysis of Calcul Infinitesimal

Dennis M. Cates

Published November 22nd 2011
ISBN :
Hardcover
616 pages
Enter the sum

 About the Book 

A Guide to Cauchys Calculus follows Augustin-Louis Cauchys development of the rigorous version of calculus we are taught today in an introductory calculus sequence. Cauchys original 1823 text (his first devoted to calculus), Résumé des leçonsMoreA Guide to Cauchys Calculusfollows Augustin-Louis Cauchys development of the rigorous version of calculus we are taught today in an introductory calculus sequence. Cauchys original 1823 text (his first devoted to calculus), Résumé des leçons sur le calcul infinitésimal, Summary of Lectures on the Infinitesimal Calculus, is the central focus of this book and will be studied in depth. Contained here are the complete English translations of the relevant lectures within Cauchys text covering his real, single variable, differential and integral calculus. In addition, a simply written line-by-line explanation for each of Cauchys lectures is included which clarifies his thinking and his proofs, solves his example problems, discusses his misconceptions, and contains supplemental proofs of fundamental concepts Cauchy felt were self-evident. Comparisons between Cauchys method of presentation and a modern treatment are made throughout the book by including todays standard definitions and proofs of the fundamental theorems of the calculus alongside those developed by Cauchy in his text. In total, this book will serve as a complete resource for anyone who teaches calculus or is interested in fully understanding the first calculus sequence at the high school or college level.