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Mathematical Preliminaries And Error Analysis | |
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Introduction | |
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Review of Calculus | |
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Round-off Error and Computer Arithmetic | |
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Errors in Scientific Computation | |
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Computer Software | |
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Solutions Of Equations Of One Variable | |
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Introduction | |
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The Bisection Method | |
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The Secant Method | |
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Newton's Method | |
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Error Analysis and Accelerating Convergence | |
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M ller's Method | |
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Survey of Methods and Software | |
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Interpolation And Polynomial Approximation | |
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Introduction | |
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Lagrange Polynomials | |
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Divided Differences | |
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Hermite Interpolation | |
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Spline Interpolation | |
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Parametric Curves | |
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Survey of Methods and Software | |
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Numerical Integration And Differentiation | |
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Introduction | |
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Basic Quadrature Rules | |
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Composite Quadrature Rules | |
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Romberg Integration | |
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Gaussian Quadrature | |
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Adaptive Quadrature | |
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Multiple Integrals | |
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Improper Integrals | |
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Numerical Differentiation | |
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Survey of Methods and Software | |
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Numerical Solution Of Initial-Value Problems | |
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Introduction | |
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Taylor Methods | |
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Runge-Kutta Methods | |
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Predictor-Corrector Methods | |
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Extrapolation Methods | |
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Adaptive Techniques | |
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Methods for Systems of Equations | |
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Stiff Differentials Equations | |
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Survey of Methods and Software | |
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Direct Methods For Solving Linear Systems | |
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Introduction | |
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Gaussian Elimination | |
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Pivoting Strategies | |
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Linear Algebra and Matrix Inversion | |
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Matrix Factorization | |
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Techniques for Special Matrices | |
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Survey of Methods and Software | |
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Iterative Methods For Solving Linear Systems | |
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Introduction | |
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Convergence of Vectors | |
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Eigenvalues and Eigenvectors | |
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Conjugate Gradient Methods | |
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The Jacobi and Gauss-Seidel Methods | |
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The SOR Method | |
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Error Bounds and Iterative Refinement | |
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Survey of Methods and Software | |
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Approximation Theory | |
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Introduction | |
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Discrete Least Squares Approximation | |
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Continuous Least Squares Approximation | |
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Chebyshev Polynomials | |
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Rational Function Approximation | |
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Trigonometric Polynomial Approximation | |
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Fast Fourier Transforms | |
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Survey of Methods and Software | |
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Approximating Eigenvalues | |
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Introduction | |
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Isolating Eigenvalues | |
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The Power Method | |
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Householder's Method | |
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The QR Method | |
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Survey of Methods and Software | |
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Solutions Of Systems Of Nonlinear Equations | |
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Introduction | |
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Newton's Methods for Systems | |
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Quasi-Newton Methods | |
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The Steepest Descent Method | |
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Survey of Methods and Software | |
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Homotopy and Continuation Methods | |
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Boundary-Value Problems For Ordinary Differential Equations | |
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Introduction | |
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The Linear Shooting Method | |
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Linear Finite Difference Methods | |
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The Nonlinear Shooting Method | |
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Nonlinear Finite-Difference Methods | |
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Variational Techniques | |
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Survey of Methods and Software | |
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Numerical Methods For Partial Differential Equations | |
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Introduction | |
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Finite-Difference Methods for Elliptic Problems | |
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Finite-Difference Methods for Parabolic Problems | |
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Finite-Difference Methods for Hyperbolic Problems | |
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Introduction to the Finite-Element Method | |
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Survey of Methods and Software. | |