This book is a complete English translation of Augustin-Louis Cauchy's historic 1823 text (his
first devoted to calculus) Résumé des leçons sur le calcul infinitésimal Summary of Lectures
on the Infinitesimal Calculus originally written to benefit his École 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.
