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Mathematical Preliminaries and Error Analysis | |
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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 | |
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Fixed-Point Iteration | |
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Newton's Method and its Extensions | |
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Error Analysis for Iterative Methods | |
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Accelerating Convergence | |
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Zeros of Polynomials and 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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Interpolation and the Lagrange Polynomial | |
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Data Approximation and Neville's Method | |
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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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Intial-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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Multistep Methods | |
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Variable Step-Size Multistep Methods | |
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Extrapolation Methods | |
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Higher-Order Equations and Systems of Differential Equations | |
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Stability | |
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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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The Jacobi and Gauss-Siedel Iterative Techniques | |
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Iterative Techniques for Solving Linear Systems | |
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Relaxation 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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Orthogonal Matrices and Similarity Transformations | |
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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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Singular Value Decomposition | |
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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 | |