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Cauchy's Calcul infinitésimal : an annotated English translation

Author: Augustin Louis Cauchy, Baron; Dennis M Cates
Publisher: Cham, Switzerland : Springer, [2019]
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Cates, Dennis M.
Cauchy's Calcul Infinitésimal : An Annotated English Translation.
Cham : Springer, ©2019
Named Person: Augustin Louis Cauchy, Baron; Augustin Louis Cauchy, Baron
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Augustin Louis Cauchy, Baron; Dennis M Cates
ISBN: 9783030110369 3030110362
OCLC Number: 1096527930
Language Note: Translated from French.
Notes: 14 METHODS THAT WORK TO SIMPLIFY THE STUDY OF TOTAL DIFFERENTIALS FOR FUNCTIONS OF SEVERAL INDEPENDENT VARIABLES. SYMBOLIC VALUES OF THESE DIFFERENTIALS.
Description: 1 online resource (265 pages)
Contents: Intro; Translator's Preface; A Few Notes Regarding Cauchy's Original Works:; A Few Technical Notes Regarding This Translation:; A Few Final Thoughts:; SUMMARY OF LECTURES; FOREWORD. ERRATA. This is the original errata sheet included in the 1823 publication. All of these errors have been corrected in this translation along with added footnotes wherever a change has been made. The corrections on pages 37 and 47 (these are page references to Cauchy's original text) are due to slightly different characters or symbols being used. The variations between what was actually used for the printing and the corrected versions are slight-perhaps an odd typeset in use at the time. TABLE OF CONTENTS.; Part I DIFFERENTIAL CALCULUS. 1 OF VARIABLES, THEIR LIMITS, AND INFINITELY SMALL QUANTITIES. 2 OF CONTINUOUS AND DISCONTINUOUS FUNCTIONS. GEOMETRIC REPRESENTATION OF CONTINUOUS FUNCTIONS.; 3 DERIVATIVES OF FUNCTIONS OF A SINGLE VARIABLE.; 4 DIFFERENTIALS OF FUNCTIONS OF A SINGLE VARIABLE.; 5 THE DIFFERENTIAL OF THE SUM OF SEVERAL FUNCTIONS IS THE SUM OF THEIR DIFFERENTIALS. CONSEQUENCES OF THIS PRINCIPLE. DIFFERENTIALS OF IMAGINARY FUNCTIONS. 6 USE OF DIFFERENTIALS AND DERIVED FUNCTIONS IN THE SOLUTION OF SEVERAL PROBLEMS. MAXIMA AND MINIMA OF FUNCTIONS OF A SINGLE VARIABLE. VALUES OF FRACTIONS WHICH ARE PRESENTED UNDER THE FORM 00.7 VALUES OF SOME EXPRESSIONS WHICH ARE PRESENTED UNDER THE INDETERMINATE FORM inftyinfty, infty0 ... A RELATIONSHIP WHICH EXISTS BETWEEN THE RATIO OF FINITE DIFFERENCES AND THE DERIVED FUNCTION.; 8 DIFFERENTIALS OF FUNCTIONS OF SEVERAL VARIABLES. PARTIAL DERIVATIVES AND PARTIAL DIFFERENTIALS. 9 USE OF PARTIAL DERIVATIVES IN THE DIFFERENTIATION OF COMPOSED FUNCTIONS. DIFFERENTIALS OF IMPLICIT FUNCTIONS. 10 THEOREM OF HOMOGENEOUS FUNCTIONS. MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES.; 11 USE OF INDETERMINATE FACTORS IN THE STUDY OF MAXIMA AND MINIMA.; 12 DIFFERENTIALS AND DERIVATIVES OF VARIOUS ORDERS FOR FUNCTIONS OF A SINGLE VARIABLE. CHANGE OF THE INDEPENDENT VARIABLE.; 13 DIFFERENTIALS OF VARIOUS ORDERS FOR FUNCTIONS OF SEVERAL VARIABLES.
Other Titles: Résumé des leçons données a l'Ecole royale polytechnique, sur le calcul infinitésimal.
Calcul infinitésimal
Responsibility: Dennis M. Cates.

Abstract:

This book is a complete English translation of Augustin-Louis Cauchy's historic 1823 text (his first devoted to calculus), Resume des lecons sur le calcul infinitesimal, "Summary of Lectures on the  Read more...

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"This book is a very welcome contribution. I will be using it as a source for student readings in my history of mathematics classes." (Fernando Q. Gouvea, MAA Reviews, 19 May, 2019)

 
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