New Age Principles of Real Analysis 5th Edition

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. 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 Cantor's Theory of Real Numbers. Corrections have been made wherever necessary.