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Contents: - 1. Basic Concepts and Preliminaries 2. Numbers: Real and Complex 3. Cardinality of Sets and One-to-One Correspondence 4. Analytical (Metric) Properties of R and C 5. Sequences and Subsequences (R and C) 6. Infinite Series. (R and C) 7. Limits 8. Continuous Functions 9. Differentiable Functions 10. The Riemann Integral and Darboux Integral 11. Bounded Variation and Rectification 12. Improper Integral (The Generalised Riemann Integral) 13. Sequence of Functions 14. Series of Functions 15. Power Series 16. Fourier Series, Integrals and Transforms 17. Complex Numbers and Functions, Conformal Mapping and Analytic Functions 18. Complex Integration 19. Power Series and Taylor Series 20. Laurent Series 21. Metric Spaces, Compactness and Connectedness. What's special / Useful in this book: -This textbook is envisaged to provide coherent and compressive coverage of Fundamentals of Mathematical Analysis. It is intended to serve as a text in mathematical analysis for the B.A., B.Sc. (Hons), Postgraduate, Ph.D. and Research Scholar students at various universities. This book is very helpful for theoretical understanding as well as for research usage. The main highlights of the book are: Basic Concepts and Preliminaries Numbers: Real and Complex, Cardinality of Sets and One-to-One Correspondence Analytical (Metric) Properties of R & C, Sequences and Subsequences (R & C) and Infinite Series (R & C) Limits, Continuous Functions and Differentiable Functions The Riemann Integral and Darboux Integral, Bounded Variation and Rectification Improper Integral (The Generalised Riemann Integral) and Complex Integration Sequence of Functions, Series of Functions Power Series, Fourier Series, Integrals and Transforms, Taylor Series, Laurent Series Complex Numbers and Functions, Conformal Mapping and Analytic Functions Metric Spaces, Compactness and Connectedness .
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