Introduction to Numerical Analysis

About this book

A clear, concise, modern text for the introductory numerical analysis market, stressing computer skills and real application. It aims to give students who are unfamiliar with, inexperienced and uncertain about using numerical methods, an introduction to the more basic theoretical elements of the subject allied with the generation of some practical skills for using the methods developed in the text.

Contents

1. Introduction: Why Numerical Methods? 2. Terminology 3. Taylor Series 4. Taylor's Theorem 5. Maclaurin Series 6. Basic Computer Arithmetic and Methods 7. Representation of Numbers 8. Error Measures 9. Truncation Errors 10. Computer Errors 11. Error Accumulation 12. Recurrence Relations and Error Propagation Roots of f(x)=0 13. Preliminaries Locating Roots 14. Bracketing Methods 15. Fixed Point Methods 16. Other Methods 17. Roots of Polynomials Solutions of Ax=b 18. Preliminaries 19. Diagonal Systems 20. Triangular Systems and Backward Substitution 21. Square Systems and Forward Elimination 22. Partial Pivoting 23. Operation Count 24. Jaccobi Iteration 25. Analysis of Convergence 26. Gauss-Seidel Iteration 27. Successive Over-Relaxation (SOR) 28. Numerical Differentiation 29. Preliminaries 30. Approximating First Derivatives 31. Analysis of Errors 32. Higher Order Derivatives 33. Extrapolation Numerical Integration 34. Newton-Cotes Rules 35. Preliminaries 36. Rectangular Rules 37. Reiman Sums 38. Error Analysis for Rectangular Rules 39. Trapezoidal Rule 40. Construction and Error 41. Mid-Point Rule 42. Simpson's Rule 43.Extrapolation 44. Romberg Integration Polynomial Interpolation 45. Preliminaries 46. Linear interpolation 47. Quadratic Interpolation 48. General Formula 49. Lagrange Interpolation 52. Divided Difference Interpolation 53. Equi-Spaced Interpolation 54. Other Interpolation Methods Runge-Kutta Methods for Ordinary Differential Equations 55. Preliminaries 56. Difference Equations 57. Taylor Series Methods 58. Runge-Kutta Methods 59. Local Truncation Error and Consistency 60. Global Error and Convergence 61. Numerical Stability 62. Appendices

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