A Course of Mathematical Analysis (Vols 1 and 2) – Nikolsky

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

Volume 1 here

Volume 2 here

 

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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1 Response to A Course of Mathematical Analysis (Vols 1 and 2) – Nikolsky

  1. Pingback: A Course of Mathematical Analysis (Vols 1 and 2) – Nikolsky | Chet Aero Marine

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