Cauchy's Calcul Infinitésimal, 1st ed. 2019 An Annotated English Translation
Langue : Anglais
Auteur : Cates Dennis M.
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.
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.
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.
The first English translation of Résumé des leçons sur le calcul infinitésimal
Complete with annotations throughout
Allows wider audience to experience Cauchy's original, complete text on calculus
Provides historical supplement to traditional calculus texts
Date de parution : 04-2019
Ouvrage de 267 p.
15.5x23.5 cm
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