Principles of Real Analysis

Discusses the theory from its very beginning; Foundations have been laid very carefully and the treatment is rigorous, and on modern lines; The Riemann integration is treated in full; Large number of well graded examples have been given and some of these have been solved.

The book has been made more illustrative and self-contained so as to cater to the need of students and teachers at graduate and postgraduate level. It is also meant for engineering students and other professionals as well as competitive examinations. To reinforce and solidify the understanding, some of the chapters have been rearranged and several new exercises and solved examples have been incorporated. The section on limits inferior and superior of sequences is introduced and discussed in detail. Every care has been taken to explain and elucidate the different concepts so as to provide conceptual clarity to the readers.

Table of Contents: Real Numbers/Limit Points: Open and Closed Sets/ Real Sequences/ Infinite Series/ Functions with Interval as Domain (I)/ Functions with Interval as Domain (II)/ Applications of Taylor's Theorem/ Elementary Functions/ The Riemann Integral/ The Riemann-Stieltjes Integral/ Functions of Several Variables/ Implicit Functions/ Appendix I - Theorems on Rearrangement of Terms and Tests for Arbitrary Series/ Appendix II - Cantor's Theory of Real Numbers

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The author was a Senior Lecturer in the Dept of Mathematics, SGTB Khalsa College, University of Delhi, India. He has taught undergraduate and graduate courses for more than three decades.