ebook9783030110369d4325

Description

This book is a complete English translation of Augustin-Louis Cauchy’s historic 1823¬†text (his first devoted to calculus),¬†R√©sum√©¬†des le√ßons sur le calcul infinit√©simal, “Summary of¬†Lectures on the Infinitesimal Calculus,” originally written to benefit his √âcole Polytechnique students¬†in Paris. Within this single text, Cauchy succinctly lays out and rigorously develops all of the topics¬†one encounters in an introductory study of the calculus, from his classic definition of the limit to¬†his detailed analysis of the convergence properties of infinite series. In between, the reader will¬†find a full treatment of differential and integral calculus, including the main theorems of calculus¬†and detailed methods of differentiating and integrating a wide variety of functions. Real, single¬†variable calculus is the main focus of the text, but Cauchy spends ample time exploring the¬†extension of his rigorous development to include functions of multiple variables as well as¬†complex functions. This translation maintains the same notation and terminology of Cauchy’s original work in the¬†hope of delivering as honest and true a Cauchy experience as possible so that the modern reader¬†can experience his work as it may have been like 200 years ago. This book can be used with¬†advantage today by anyone interested in the history of the calculus and analysis. In addition, it¬†will serve as a particularly valuable supplement to a traditional calculus text for those readers who¬†desire a way to create more texture in a conventional calculus class through the introduction of¬†original historical sources.¬†