Real Analysis

Contents: Preface. 1. Natural Number. 2. Real and Complex Numbers. 3. Sequences. 4. Infinite Series. 5. Harmonic Series. 6. Power Series. 7. Fourier Series. 8. Cauchy Convergence. 9. Limits and Continuity. 10. Differential Calculus. 11. Differentiability. 12. Techniques of Integration. 13. Improper Integrals. 14. Multivariable Calculus. 15. Laplace Transforms. Bibliography. Index.

Real Analysis or theory of functions of a real variable is a significant branch, dealing with the set of real numbers. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real numbers and continuity, smoothness and related properties of real-valued functions. Real analysis is an area of analysis, which studies concepts, such as sequences and their limits, continuity, differentiation, integration and sequences of functions. By definition, real analysis of focuses on the real numbers, often including positive or negative infinity. The real numbers have several important lattice-theoretic properties that are absent in the complex numbers. Most importantly, the real numbers form an ordered filed, in which addition and multiplication preserve positivity.

Present book covers all dimensions of the subject, particularly aimed at the students, who intend to master in this field of Mathematics. This book is an asset for all scholars, researchers and students. (Jacket)