عنوان

Cauchy's Calcul infinitésimal :

3030110362

9783030110369

3030110354

9783030110352

Cauchy's Calcul infinitésimal :

[Book]

an annotated English translation /

Dennis M. Cates.

Cham, Switzerland :

Springer,

[2019]

1 online resource (265 pages)

14 METHODS THAT WORK TO SIMPLIFY THE STUDY OF TOTAL DIFFERENTIALS FOR FUNCTIONS OF SEVERAL INDEPENDENT VARIABLES. SYMBOLIC VALUES OF THESE DIFFERENTIALS.

Includes bibliographical references and index.

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.

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.

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.

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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 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.

Springer Nature

com.springer.onix.9783030110369

Cauchy's Calcul Infinitésimal : An Annotated English Translation.

9783030110352

Résumé des leçons données a l'Ecole royale polytechnique, sur le calcul infinitésimal.

Tome 1.

English

Calcul infinitésimal

Cauchy, Augustin Louis,1789-1857.

Cauchy, Augustin Louis,1789-1857.

Calculus.

Geometry, Infinitesimal.

Calculus.

Geometry, Infinitesimal.

MAT015000

PBX

PBX

Cauchy, Augustin Louis,Baron,1789-1857

Cates, Dennis M.

20200823082715.0

pn

[Book]

Y