Cauchy's Calcul Infinitésimal An Annotated English Translation /: An Annotated English Translation. (2019)

• Record Type: Book
• Further Information: Note: Dennis M. Cates.
• Other Names: Cates, Dennis M
• 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.
• Publisher Details: Cham : Springer
• Publication Date: 2019
• Extent: 1 online resource (265 p.)
• Subjects: 515; Calculus; Geometry, Infinitesimal; Electronic books
• Languages: English
• ISBNs: 9783030110369; 3030110362
• Related ISBNs: 3030110354; 9783030110352
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.