Real Analysis (2 Vols-Set)

Contents: Part I: 1. Introduction of Numbers. 2. Sequences and Series. 3. Limits and Continuity. 4. Sequences and Series of functions. 5. Differentiation of functions. 6. Integration - RS integrals. 7. Different Special Functions. 8. Functions of Several Variables – Differentiation. 9. Functions of Several Variables – Integration. References. Part II: 1. Families of Sets 1–20. 2. Measurable Functions and Convergence Theorems. 3. Signed Measures and Radon Nikodym Theorem. 4. Concepts of Functional Analysis. 5. LP Spaces and some Inequalities. 6. Integration - RS Integrals. 7. Radon Measures. 8. Elements of Fourier Analysis. References.

Real Analysis, in general deals with the convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity and interchange of limit operations. It teaches an understanding about theorems and helps in construction of proofs for the theorems. The principal goal of this book “Real Analysis, Part-1” is to provide the reader with a comprehensive knowledge of Real Analysis. This book is written in a user-friendly manner to make the material easy to understand by the reader. The proofs of the theorems are written clearly and informally as possible. The book has been designed to cater the need and requirement of Undergraduate, Postgraduate and Doctoral students of science, and engineering discipline in University and Colleges.