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
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
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