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| Mathematical preliminaries | |
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| Review of Calculus | |
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| Round-off Errors and Computer Arithmetic | |
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| Algorithms and Convergence | |
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| Numerical Software | |
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| Solutions of equations in one variable | |
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| The Bisection Method. Fixed-Point Iteration | |
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| The Newton's Method | |
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| Error Analysis for Iterative Methods | |
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| Accelerating Convergence | |
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| Zeros of Polynomials and Muller's Method | |
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| Survey of Methods and Software | |
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| Interpolation and polynomial approximation | |
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| Interpolation and the LaGrange Polynomial | |
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| Divided Differences | |
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| Hermite Interpolation | |
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| Cubic Spline Interpolation | |
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| Parametric Curves | |
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| Survey of Methods and Software | |
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| Numerical differentiation and integration | |
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| Numerical Differentiation | |
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| Richardson's Extrapolation | |
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| Elements of Numerical Integration | |
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| Composite Numerical Integration | |
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| Romberg Integration | |
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| Adaptive Quadrature Methods | |
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| Gaussian Quadrature | |
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| Multiple Integrals | |
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| Improper Integrals | |
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| Survey of Methods and Software | |
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| Initial-value problems for ordinary differential equations | |
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| The Elementary Theory of Initial-Value Problems | |
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| Euler's Method | |
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| Higher-Order Taylor Methods | |
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| Runge-Kutta Methods | |
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| Error Control and the Runge-Kutta-Fehlberg Method | |
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| Multi-Step Methods | |
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| Variable Step-Size Multi-Step Methods | |
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| Extrapolation Methods | |
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| Higher-Order Equations and Systems of Differential Equations | |
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| Stability. Stiff Differential Equations | |
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| Survey of Methods and Software | |
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| Direct methods for solving linear systems | |
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| Linear Systems of Equations | |
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| Pivoting Strategies | |
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| Linear Algebra and Matrix Inversion | |
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| The Determinant of a Matrix | |
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| Matrix Factorization | |
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| Special Types of Matrices | |
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| Survey of Methods and Software | |
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| Iterative techniques in matrix algebra | |
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| Norms of Vectors and Matrices | |
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| Eigenvalues and Eigenvectors | |
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| Iterative Techniques for Solving Linear Systems | |
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| Error Bounds and Iterative Refinement | |
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| The Conjugate Gradient Method | |
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| Survey of Methods and Software | |
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| Approximation theory | |
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| Discrete Least Squares Approximation | |
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| Orthogonal Polynomials and Least Squares Approximation | |
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| Chebyshev Polynomials and Economization of Power Series | |
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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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| Linear Algebra and Eigenvalues | |
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| The Power Method | |
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| Householder's Method | |
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| The QR Algorithm | |
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| Survey of Methods and Software | |
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| Numerical solutions of nonlinear systems of equations | |
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| Fixed Points for Functions of Several Variables | |
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| Newton's Method | |
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| Quasi-Newton Methods | |
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| Steepest Descent Techniques | |
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| Homotopy and Continuation Methods | |
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| Survey of Methods and Software | |
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| Boundary-value problems for ordinary differential equations | |
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| The Linear Shooting Method | |
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| The Shooting Method for Nonlinear Problems | |
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| Finite-Difference Methods for Linear Problems | |
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| Finite-Difference Methods for Nonlinear Problems | |
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| The Rayleigh-Ritz Method | |
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| Survey of Methods and Software | |
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| Numerical solutions to partial differential equations | |
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| Elliptic Partial-Differential Equations | |
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| Parabolic Partial-Differential Equations | |
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| Hyperbolic Partial-Differential Equations | |
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| An Introduction to the Finite-Element Method | |
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| Survey of Methods and Software | |
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| Bibliography | |
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| Answers to Selected Exercises | |
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| Index | |