A course of mathematical analysis. Vol. 1-2 → Обява 46191545

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

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