Real Analysis

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This revised edition provides an excellent introduction to topics in Real Analysis through an elaborate exposition of all fundamental concepts and results. The treatment is rigorous and exhaustive-both classical and modern topics are presented in a lucid manner in order to make this text appealing to students. Clear explanations, many detailed worked examples and several challenging ones included in the exercises, enable students to develop problem-solving skills and foster critical thinking. The coverage of the book is incredibly comprehensive, with due emphasis on Lebesgue theory, metric spaces, uniform convergence, Riemann–Stieltjes integral, multi-variable theory, Fourier series, improper integration, and parametric integration. The book is suitable for a complete course in real analysis at the advanced undergraduate or postgraduate level. About The Author DIPAK CHATTERJEE, Ph.D., is Principal, Institute of Engineering and Management, Kolkata. Earlier, he served as distinguished professor of mathematics at St. Xavier’s college, Kolkata and also visiting professor at many universities, engineering colleges, and management institutions. He has several years of experience of teaching undergraduate and postgraduate students. Dr. Chatterjee has contributed a large number of research articles in different journals and also authored several textbooks.  Table Of Contents Preface Preface To The First Edition 1. Real Number System 2. Sequences And Series 3. Real Function, Limit And Continuity 4. Differentiability And Derivability 5. Mean Value Theorems 6. Riemann Integration 7. Uniform Convergence 8. Power Series 9. Semi-Continuous Functions 10. Parametric Integration 11. Fourier Series 12. Improper Integral 13. Multivariable Theory 14. Multiple Integral 15. Double Sequence And Series 16. Functions Of Bounded Variation 17. Riemann–Stieltjes Integral 18. Metric Spaces 19. Lebesgue Theory Bibliography Index