In this post we will see the two volume *Course in Mathematical*

*Analysis* by *S. M. Nikolsky.*

# About the book

The major part of this two-volume textbook stems from the

course in mathematical analysis given by the author for many

years at the Moscow Physico-technical Institute.The first volume consisting of eleven chapters includes an

introduction (Chapter 1)which treats of fundamental notions of

mathematical analysis using an intuitive concept of a limit. With

the aid of visual interpretation and some considerations of a

physical character it establishes the relationship between the

derivative and the integral and gives some elements of differentiation and integration techniques necessary to those readers who are simultaneously studying physics.The notion of a real number is interpreted in the first volume

(Chapter 2) on the basis of its representation as an infinite decimal. Chapters 3-11 contain the following topics: Limit of Sequence, Limit of Function, Functions of One Variable, Functions of Several Variables, Indefinite Integral, Definite Integral, Some Applications of Integrals, Series.Volume 2 contains multiple integrals, field theory. Fourier series and Fourier integral, differential manifolds and differential forms, and the Lebesgue integral.

The books were translated from the Russian by *V. M. Volosov.* The

book was published by first Mir Publishers in 1977 with reprints in

1981, 1985 and 1987. The second volume below is from the 1987 print, while the first one is from 1977 one.

Note: Volume 2 is at a much better scan resolution. In an earlier post we had seen only Vol. 2, that post had dead links. This post with both volumes has cleaned scans and updated links. Earlier post has been updated.

Credits to the original uploaders*.*

You can get

# Contents

# Volume 1

## Preface to the English Edition 5

## Chapter 1. Introduction 13

## Chapter 2. Real Numbers 45

## Chapter 3. Limit of Sequence 68

## Chapter 4. Limit of Function 90

## Chapter 5. Differential Calculus. Functions of One Variable 127

## Chapter 6. n-dimensional Space. Geometrical Properties of Curves 180

## Chapter 7. Differential Calculus. Functions of Several Variables 215

## Chapter 8. Indefinite Integral. Properties of Polynomials 314

## Chapter 9. Definite Integral 351

## Chapter 10. Some applications of integral. Approximate Methods 395

## Chapter 11. Series 417

## Name Index 453

## Subject Index 455

# Volume 2

## Chapter 12. Multiple Integrals 9

## Chapter 13. Scalar and Vector Fields. Differentiation and Integration

of Integral with Respect to Parameter. Improper Integrals 80

## Chapter 14. Normed Linear Spaces. Orthogonal Systems 147

## Chapter 15. Fourier Series. Approximation of Functions with Polynomials 188

## Chapter 16. Fourier Integral. Generalized Functions 240

## Chapter 17. Differentiable Manifolds and Differential Forms 289

## Chapter 18. Supplementary Topics 326

## Chapter 19. Lebesgue Integral 338

## Name Index 437

Subject Index 438

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