Principles of Real Analysis by Malik, S.C

		Principles of Real Analysis Malik, S.C. , Senior Lecturer, Department of Mathematics, S.G.T.B. Khalsa College, University of Delhi, Delhi.
		PRINTED BOOK DETAILS: ISBN : 978-81-224-3276-3 Publication Year : 2011 Edition : 3rd Reprint : Apr, 2012 Pages : 388 Price : Rs. 275.00  Binding : Paperback

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. About the Author: S.C. Malik was a Senior Lecturer in the Department of Mathematics, S.G.T.B. Khalsa College, University of Delhi, 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 Taylor's Theorm  Elementary Functions The Riemann Integral The Riemann-Stieltjes Integral Functions of Several Variables Implicit Functions