Principles of Real Analysis Book

This 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 Dedekin'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 form; and, elementary functions. The Riemann integration is treated full. Finally, it deals with Riemann-Stieltjes integrals; functions of several variables; implicit functions; and, Jacobians and the method of Lagrange's multipliers for extreme values of functions with subsidiary condition. The material on functions of two-variables has been given with more details and more examples. An appendix has 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.Read More