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Principles of Real Analysis

Principles of Real Analysis

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The book is intended to serve as a textbook for a course in Real Analysis for honours and postgraduate students of various universities. It is also meant for engineering students and other professionals as well as competitive examinations. 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 starts with a quick review of the essential properties of rational numbers and using Dedekinds form, the properties for real numbers are established. This foundation supports the subsequent chapters-topological framework; sequences and series; continuity; differentiation; extreme values; indeterminate forms; elementary functions. The Riemann integration is treated full. Finally, it deals with Riemann-Stieltjes integrals; Functions of several variables; Implicit functions; Jacobians and the method of Lagranges multipliers for extreme values of functions with subsidiary conditions. The material on functions of two-variables has been given with more details and more examples. The salient feature of the book is that a large number of well graded examples have been given and some of them have been solved for the benefit of the readers. The fifth multicolour edition of this book has been prepared with a few additional features. It includes two appendices-Theorems on Rearrangement of Terms and Tests for Arbitrary Series and Cantors Theory of Real Numbers. Corrections have been made wherever necessary. About the Author S C Malik was a Senior Lecturer in the Department of Mathematics, SGTB Khalsa College, University of Delhi, Delhi. He has taught undergraduate and postgraduate analysis courses for more than three decades.

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About the Book

The book is intended to serve as a textbook for a course in Real Analysis for honours and postgraduate students of Indian universities. It is also meant for engineering students and other professionals as well as competitive examinations.

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 starts with a quick review of the essential properties of rational numbers and using Dedekind's form, the properties for real numbers are established. This foundation supports the subsequent chapters—topological framework; sequences and series; continuity; differentiation; extreme values; indeterminate forms; elementary functions. The Riemann integration is treated full. Finally, it deals with Riemann-Stieltjes integrals; functions of several variables; implicit functions; Jacobians and the method of Lagrange's multipliers for extreme values of functions with subsidiary conditions. The material on functions of two-variables has been given with more details and more examples. An appendix has also been given on Cantor's theory of the construction of real numbers to make the book more useful. The salient feature of the book is that a large number of well graded examples have been given and some of them have been solved for the benefit of the readers.

This edition is for sale in India, Bangladesh, Bhutan, Maldives, Nepal, Myanmar, Pakistan and Sri Lanka only.


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Product Details
  • ISBN-13: 9789385923852
  • Publisher: New Age International Private Limited
  • Binding: Paperback
  • Language: English
  • Weight: 521.63 gr
  • ISBN-10: 9385923854
  • Publisher Date: 01 Jan 2017
  • Height: 16.002 mm
  • No of Pages: 382
  • Width: 174 mm

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