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.

Contents

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