Numerical Analysis

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The text is designed keeping in mind the course taken up by PG students. It presents Fundamental Theory & Numerical Derivation of relevant Equations, which is followed by numerous Solved Examples & Supplementary Problems for Practice. Key Features Exhaustive Table of Contents spanning over 30 Chapters Classical & Historical Introductory topics included: "Classical Numerical Analysis" [Features in all standard syllabi] More than 90% Coverage to all major topics: Laplace transformation, Calculus, Errors, Algebra, Polynomial interpolation, Iterative methods, Numerical differentiation, Numerical integration [Comprises 45% of any standard syllabi] Inclusion of important topics : Fast Fourier transforms, Finite elements, Differential equations [Features in standard text as well] Pedagogy Illustrations : 156 (Figures: 83 & Tables: 73) Solved problems: 804 683 Supplementary problems Table of Content Chapter 1. What is Numerical Analysis? Chapter 2. The Collocation Polynomial Chapter 3. Finite Differences Chapter 4. Factorial Polynomials Chapter 5. Summation Chapter 6. The Newton Formula Chapter 7. Operators and Collocation Polynomials Chapter 8.Unequally Spaced Arguments Chapter 9. Splines Chapter 10. Osculating Polynomials Chapter 11. The Taylor Polynomial Chapter 12. Interpolation Chapter 13. Numerical Differentiation Chapter 14. Numerical Integration Chapter 15. Gaussian Integration Chapter 16. Singular Integrals Chapter 17. Sums and Series Chapter 18. Difference Equations Chapter 19. Differential Equations Chapter 20. Differential Problems of Higher Order Chapter 21. Least-Squares Polynomial Approximation Chapter 22. Min-Max Polynomial Approximation Chapter 23. Approximation by Rational Functions Chapter 24. Trigonometric Approximation Chapter 25. Nonlinear Algebra Chapter 26. Linear Systems Chapter 27. Linear Programming Chapter 28. Overdetermined Systems Chapter 29. Boundary Value Problems Chapter 30. Monte Carlo Methods Answers to Supplementary Problems