Mathematical Analysis

This book is intended to serve as a text in Mathematical Analysis for the undergraduate and postgraduate students of various universities. Professionals will also find this book useful. The book has theory from its very beginning. The foundations have been laid very carefully and the treatment is rigorous based on modern lines. It opens with a brief outline of the essential properties of rational numbers and using Dedekind's cut, the properties of real numbers are also established. This foundation supports the subsequent chapters: Topological Framework Real Sequences and Series, Continuity, Differentiation, Functions of Several Variables, Elementary and Implicit Functions, Riemann and Riemann-Stieltjes Integrals, Lebesgue Integrals, Surface, Double and Triple Integrals are discussed in detail. Uniform Convergence, Power Series, Fourier Series, Improper Integrals have been presented in as simple and lucid manner as possible. Number of solved examples to illustrate various types have also been included. As per need, in the present atmosphere, a chapter on Metric Spaces discussing completeness, compactness and connectedness of the spaces has been added. Finally, two appendices discussing Beta-Gamma functions, and Cantor's theory of real numbers, add glory to the contents of the book. -- Provided by publisher