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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. | |