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| Preliminaries | |
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| Analysis versus Numerical Analysis | |
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| Computers and Numerical Analysis | |
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| An Illustrative Example | |
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| Kinds of Errors in Numerical Procedures | |
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| Interval Arithmetic | |
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| Parallel and Distributed Computing | |
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| Measuring the Efficiency of Procedures | |
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| Solving Nonlinear Equations | |
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| Interval Halving (Bisection) | |
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| Linear Interpolation Methods | |
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| Newton's Method | |
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| Muller's Method | |
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| Fixed-Point Iteration | |
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| Other Methods | |
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| Nonlinear Systems | |
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| Solving Sets of Equations | |
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| Matrices and Vectors | |
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| Elimination Methods | |
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| The Inverse of a Matrix and Matrix Pathology | |
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| Almost Singular Matrices - Condition Numbers | |
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| Interactive Methods | |
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| Parallel Processing | |
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| Interpolation and Curve Fitting | |
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| Interpolating Polynomials | |
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| Divided Differences | |
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| Spline Curves | |
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| Bezier Curves and B-Splines | |
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| Interpolating on a Surface | |
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| Least Squares Approximations | |
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| Approximation of Functions | |
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| Chebyshev Polynomials and Chebyshev Series | |
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| Rational Function Approximations | |
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| Fourier Series | |
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| Numerical Differentiation and Integration | |
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| Differentiation with a Computer | |
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| Numerical Integration - The Trapezoidal Rule | |
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| Simpson's Rules | |
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| An Application of Numerical Integration - Fourier Series and Fourier Transforms Adaptive Integration | |
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| Gaussian Quadrature | |
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| Multiple Integrals | |
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| Applications of Cubic Splines | |
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| Numerical Solution of Ordinary Differential Equations | |
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| The Taylor Series Method | |
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| The Euler Method and Its Modification | |
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| Runge-Kutta Methods | |
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| Multistep Methods | |
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| Higher-Order Equations and Systems | |
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| Stiff Equations | |
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| Boundary-Value Problems | |
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| Characteristic-Value Problems | |
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| Optimization | |
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| Finding the Minimum of y = f(x) | |
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| Minimizing a Function of Several Variables | |
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| Linear Programming | |
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| Nonlinear Programming | |
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| Other Optimizations | |
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| Partial Differential Equations | |
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| Elliptic Equations | |
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| Parabolic Equations | |
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| Hyperbolic Equations | |
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| Finite Element Analysis | |
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| Mathematical Background | |
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| Finite Elements for Ordinary Differential Equation | |
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| Finite Elements for Partial Differential Equation | |
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| Appendices | |
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| Some Basic Information from Calculus | |
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| Software Resources | |
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| Answers to Selected Exercises | |
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| References | |
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| Index | |