Cauchy's Calcul Infinitésimal : An Annotated English Translation. 1st ed. 2019

種類:

電子ブック

責任表示:

by Dennis M. Cates

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Cates, Dennis M.
• SpringerLink (Online service)

ISBN:

9783030110369 [3030110362]    

注記:

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 Formula
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 Polytechnic 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 sa

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