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| Introduction | |
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| Preliminary Remarks | |
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| Review of Taylor Series | |
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| Floating-Point Representation And Errors | |
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| Floating-Point Representation | |
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| Loss of Significance | |
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| Locating Roots Of Equations | |
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| Bisection Method | |
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| Newton+s Method | |
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| Secant Method | |
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| Interpolation And Numerical Differentiation | |
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| Polynomial Interpolation | |
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| Errors in Polynomial Interpolation | |
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| Estimating Derivatives and Richardson Extrapolation | |
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| Numerical Integration | |
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| Lower and Upper Sums | |
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| Trapezoid Rule | |
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| Romberg Algorithm | |
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| Additional Topics On Numerical Integration | |
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| Simpson+s Rule and Adaptive Simpson+s Rule | |
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| Gaussian Quadrature Formulas | |
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| Systems Of Linear Equations | |
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| Naive Gaussian Elimination | |
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| Gaussian Elimination with Scaled Partial Pivoting | |
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| Tridiagonal and Banded Systems | |
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| Additional Topics Concerning Systems Of Linear Equations | |
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| Matrix Factorizations | |
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| Iterative Solutions of Linear Systems | |
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| Eigenvalues and Eigenvectors | |
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| Power Method | |
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| Approximation By Spline Functions | |
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| First-Degree and Second-Degree Splines | |
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| Natural Cubic Splines | |
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| B Splines: Interpolation and Approximation | |
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| Ordinary Differential Equations | |
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| Taylor Series Methods | |
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| Runge-Kutta Methods | |
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| Stability and Adaptive Runge-Kutta and Multistep Methods | |
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| Systems Of Ordinary Differential Equations | |
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| Methods for First-Order Systems | |
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| Higher-Order Equations and Systems | |
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| Adams-Bashforth-Moulton Methods | |
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| Smoothing Of Data And The Method Of Least Squares | |
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| Method of Least Squares | |
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| Orthogonal Systems and Chebyshev Polynomials | |
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| Other Examples of the Least-Squares Principle | |
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| Monte Carlo Methods And Simulation | |
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| Random Numbers | |
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| Estimation of Areas and Volumes by Monte Carlo Techniques | |
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| Simulation | |
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| Boundary-Value Problems For Ordinary Differential Equations | |
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| Shooting Method Shooting Method Algorithm | |
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| A Discretization Method | |
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| Partial Differential Equations | |
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| Parabolic Problems | |
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| Hyperbolic Problems | |
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| Elliptic Problems | |
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| Minimization Of Functions | |
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| One-Variable Case | |
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| Multivariate Case | |
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| Linear Programming | |
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| Standard Forms and Duality | |
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| Simplex Method | |
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| Approximate Solution of Inconsistent Linear Systems | |
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| Advice On Good Programming Practices | |
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| Programming Suggestions | |
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| Representation Of Numbers In Different Bases | |
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| Representation of Numbers in Different Bases | |
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| Additional Details On Ieee Floating-Point Arithmetic | |
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| More on IEEE Standard Floating-Point Arithmetic | |
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| Linear Algebra Concepts And Notation | |
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| Elementary Concepts | |
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| Abstract Vector Spaces | |
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| Answers For Selected Problems | |
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| Bibliography | |
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| Index | |