In this post, we will see the book *Mathematical Analysis – Differentiation And Integration*

by I. G. Aramanovich; R.S.Guter; L.A.Lyusternik; I.L. Raukhvarger; M. I. Skanavi; A. R.Yanpol’skii.

# About the book

The present volume of the series in Pure and Applied Mathematics is devoted to two basic operations of mathematical analysis — differentiation and integration. It discusses the complex of problems directly connected with the operations of differentiation and integration of functions of one or several variables, in the classical sense, and also elementary generalizations of these operations. Further generalizations will be given in subsequent volumes of the series, volumes devoted to the theory of functions of real variables and to functional analysis.

Together with an earlier volume in the series, volume 69, L. A. Lyusternik and A. R. Yanpol’skii, Mathematical Analysis (Functions, Limits, Series, Continued Fractions), the present one includes material for a course of mathematical analysis, which is treated in a logically connected manner, briefly and without proofs, but with many examples worked in detail.

The book was translated from Russian by H. Moss and edited by I. N. Sneddon and was published in 1965.

Credits to original uploader.

You can get the book here.

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# Contents

## CHAPTER I. DIFFERENTIATION OF FUNCTIONS OF ONE VARIABLE 1

## CHAPTER II. DIFFERENTIATION OF FUNCTIONS OF n VARIABLES 46

## CHAPTER III. COMPOSITE AND IMPLICIT FUNCTIONS OF n VARIABLES 76

## CHAPTER IV. SYSTEMS OF FUNCTIONS AND CURVILINEAR COORDINATES IN A PLANE AND IN SPACE 99

## CHAPTER V. INTEGRATION OF FUNCTIONS 135

## CHAPTER VI. IMPROPER INTEGRALS. INTEGRALS DEPENDENT ON A PARAMETER. STIELTJES’ INTEGRAL 135

## CHAPTER VII. THE TRANSFORMATION OF DIFFERENTIAL AND INTEGRAL EXPRESSIONS 226

APPENDICES 257

REFERENCES 309

INDEX 311