About the book

The major part of this two-volume textbook, with the exception of some supplementary material, stems from the course in mathematical analysis given by the author for many years at the Moscow Physico-technical Institute.

The first chapter is an introduction. It treats of fundamental notions of mathematical analysis using an intuitive concept of a limit. Ultimately, it even establishes, with the aid of visual interpretation and some considera­ tions of a physical character, the relationship between the derivative and the integral and gives some elements of differentiation and integration tech­ niques necessary to those readers who are simultaneously studying physics.

The second chapter is devoted to the notion of a real number which is interpreted on the basis of its representation as an infinite decimal. The part of this chapter given in small print may be omitted by the reader in his first acquaintance with the subject-matter.

Contents

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