Cauchy's Calcul Infinitésimal

This book is a complete English translation of Augustin-Louis Cauchy's historic 1823text (his first devoted to calculus),Résumédes leçons sur le calcul infinitésimal, "Summary ofLectures on the Infinitesimal Calculus," originally written to benefit his École Polytechnique studentsin Paris. Within this single text, Cauchy succinctly lays out and rigorously develops all of the topicsone encounters in an introductory study of the calculus, from his classic definition of the limit tohis detailed analysis of the convergence properties of infinite series. In between, the reader willfind a full treatment of differential and integral calculus, including the main theorems of calculusand detailed methods of differentiating and integrating a wide variety of functions. Real, singlevariable calculus is the main focus of the text, but Cauchy spends ample time exploring theextension of his rigorous development to include functions of multiple variables as well ascomplex functions. This translation maintains the same notation and terminology of Cauchy's original work in thehope of delivering as honest and true a Cauchy experience as possible so that the modern readercan experience his work as it may have been like 200 years ago. This book can be used withadvantage today by anyone interested in the history of the calculus and analysis. In addition, itwill serve as a particularly valuable supplement to a traditional calculus text for those readers whodesire a way to create more texture in a conventional calculus class through the introduction oforiginal historical sources.