Principles Of Real Analysis

About the Book:
The book is intended to serve as a textbook for a course in analysis for Honours and Postgraduate students of Indian universities. It is also meant for engineering students and other professional 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 cut 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 fully. Finally, it deals with Riemann-Stieltjes integrals; functions of several variables; implict 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. An appendix has also been given on Cantors 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.


About the Author:
He was a senior lecturer in the department of mathematics at S.G.T.B. Khalsa College, University of Delhi. He had been teaching graduate and undergraduate analysis courses for more than three decades.


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 Taylors Theorem
Elementary Functions
The Riemann Integral
The Riemann-Stielties Integral
Functions of Several Variables, Implicit Functions
Appendixes
Index.