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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 | |