Mathematical Analysis

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Overview

The book is intended to serve as a text in analysis by the Honours and post-graduate students of the various universities. Professionals or those preparing for competitive examinations will also find this book useful. The book discusses the theory from its very beginning. The foundations have been laid very carefully and the treatment is rigorous and on modern lines. It opens with a brief outline of the essential properties of rational numbers and using Dedekind's cut, the properties of real numbers are ...
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Overview

The book is intended to serve as a text in analysis by the Honours and post-graduate students of the various universities. Professionals or those preparing for competitive examinations will also find this book useful. The book discusses the theory from its very beginning. The foundations have been laid very carefully and the treatment is rigorous and on modern lines. It opens with a brief outline of the essential properties of rational numbers and using Dedekind's cut, the properties of real numbers are established. This foundation supports the subsequent chapters: topological frame work real sequences and series, continuity differentiation, functions of several variables, elementary and implicit functions, Riemann and Riemann-Stieltjes integrals, Lebesgue integrals, surface, double and triple integrals are discussed in detail. Uniform convergence, Power series, Fourier series, Improper integrals have been presented in as simple and lucid manner as possible and fairly large number solved examples to illustrate various types have been introduced. As per need, in the present set up, a chapter on Metric Spaces discussing completeness, compactness and connectedness of the spaces has been added. Finally two appendices discussing Beta-Gamma functions, and Cantor's theory of real numbers add glory to the contents of the book.
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Editorial Reviews

Booknews
A text for an advanced-undergraduate/graduate course in real analysis. This revised edition (1st was in 1985) adds a chapter on metric spaces discussing completeness, compactness, and connectedness of the spaces, and two appendices discussing Beta-Gamma functions and Cantor's theory of real numbers. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9788122403237
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 1/1/1992
  • Edition number: 2
  • Pages: 903

Table of Contents

Preface to the Second Edition
Preface to the First Edition
Ch. 1 Real Numbers 1
Ch. 2 Open Sets, Closed Sets and Countable Sets 33
Ch. 3 Real Sequences 53
Ch. 4 Infinite Series 109
Ch. 5 Functions of a Single Variable (I) 154
Ch. 6 Functions of a Single Variable (II) 185
Ch. 7 Applications of Taylor's Theorem 216
Ch. 8 Functions 236
Ch. 9 The Riemann Integral 270
Ch. 10 The Riemann-Stieltjes Integral 330
Ch. 11 Improper Integrals 351
Ch. 12 Uniform Convergence 404
Ch. 13 Power Series 440
Ch. 14 Fourier Series 463
Ch. 15 Functions of Several Variables 492
Ch. 16 Implicit Functions 562
Ch. 17 Integration on R[superscript 2] 588
Ch. 18 Integration on R[superscript 3] 652
Ch. 19 Metric Spaces 726
Ch. 20 The Lebesgue Integral 811
Appendix I Beta and Gamma Functions 872
Appendix II Cantor's Theory of Real Numbers 879
Bibliography 893
Index 897
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