LEADER 04305nam 22004815 450 001 9910338255703321 005 20200701233704.0 010 $a3-030-11036-2 024 7 $a10.1007/978-3-030-11036-9 035 $a(CKB)4100000007823514 035 $a(MiAaPQ)EBC5746940 035 $a(DE-He213)978-3-030-11036-9 035 $a(PPN)235671088 035 $a(EXLCZ)994100000007823514 100 $a20190403d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCauchy's Calcul Infinitésimal $eAn Annotated English Translation /$fby Dennis M. Cates 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (265 pages) 311 $a3-030-11035-4 327 $aDifferential 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. 330 $aThis 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 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. . 606 $aMathematics 606 $aHistory 606 $aCalculus 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 606 $aCalculus$3https://scigraph.springernature.com/ontologies/product-market-codes/M12220 615 0$aMathematics. 615 0$aHistory. 615 0$aCalculus. 615 14$aHistory of Mathematical Sciences. 615 24$aCalculus. 676 $a515 700 $aCates$b Dennis M$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781293 906 $aBOOK 912 $a9910338255703321 996 $aCauchy's Calcul Infinitésimal$91732394 997 $aUNINA