A Guide to Cauchy's Calculus - A Translation and Analysis of Calcul Infinitesimal

A Guide to Cauchy's Calculus follows Augustin-Louis Cauchy's development of the rigorous version of calculus we are taught today in an introductory calculus sequence. Cauchy's 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 Cauchy's text covering his real, single variable, differential and integral calculus. In addition, a simply written line-by-line explanation for each of Cauchy's 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 Cauchy's method of presentation and a modern treatment are made throughout the book by including today's 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.