Cauchy's Calcul Infinitésimal

An Annotated English Translation
1. Auflage 2019
ISBN: 978-3-030-11035-2
Verlag: Springer Nature Switzerland

Buch, Englisch, 267 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 606 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Cates, Dennis M.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Wissenschafts- und Universitätsgeschichte

Inhaltsverzeichnis

Differential Calculus.- Lecture One.- Lecture Two.- Lecture Three.- Lecture Four.- Lecture Five.- Lecture Six.- Lecture Seven.- Lecture Eight.- Lecture Nine.- Lecture Ten.- Lecture Eleven.- Lecture Twelve.- Lecture Thirteen.- Lecture Fourteen.- Lecture Fifteen.- Lecture Sixteen.- Lecture Seventeen.- Lecture Eighteen.- Lecture Nineteen.- Lecture Twenty.- Integral Calculus.- Lecture Twenty-One.- Lecture Twenty-Two.- Lecture Twenty-Three.- Lecture Twenty-Four.- Lecture Twenty-Five.- Lecture Twenty-Six.- Lecture Twenty-Seven.- Lecture Twenty-Eight.- Lecture Twenty-Nine.- Lecture Thirty.- Lecture Thirty-One.- Lecture Thirty-Two.- Lecture Thirty-Three.- Lecture Thirty-Four.- Lecture Thirty-Five.- Lecture Thirty-Six.- Lecture Thirty-Seven.- Lecture Thirty-Eight.- Lecture Thirty-Nine.- Lecture Forty.- Addition.- Appendices.- Appendix A: Cours D'Analyse–Chapter II, §III.- Appendix C: Cours D'Analyse–Note II.- Appendix: Cours D'Analyse–Note III.- Appendix D: On the Formulas of Taylor & Maclaurin.- Appendix E: Pagination of the 1823 and 1899 Editions.- References.- Index.

Über Autor(innen)

Dennis Cates holds a Ph.D. degree in Mathematics from Arizona State University, as well as Engineering Physics and Electrical Engineering degrees from the University of California at Berkeley.