Mathematical preliminaries | |

Review of Calculus | |

Round-off Errors and Computer Arithmetic | |

Algorithms and Convergence | |

Numerical Software | |

Solutions of equations in one variable | |

The Bisection Method. Fixed-Point Iteration | |

The Newton's Method | |

Error Analysis for Iterative Methods | |

Accelerating Convergence | |

Zeros of Polynomials and Muller's Method | |

Survey of Methods and Software | |

Interpolation and polynomial approximation | |

Interpolation and the LaGrange Polynomial | |

Divided Differences | |

Hermite Interpolation | |

Cubic Spline Interpolation | |

Parametric Curves | |

Survey of Methods and Software | |

Numerical differentiation and integration | |

Numerical Differentiation | |

Richardson's Extrapolation | |

Elements of Numerical Integration | |

Composite Numerical Integration | |

Romberg Integration | |

Adaptive Quadrature Methods | |

Gaussian Quadrature | |

Multiple Integrals | |

Improper Integrals | |

Survey of Methods and Software | |

Initial-value problems for ordinary differential equations | |

The Elementary Theory of Initial-Value Problems | |

Euler's Method | |

Higher-Order Taylor Methods | |

Runge-Kutta Methods | |

Error Control and the Runge-Kutta-Fehlberg Method | |

Multi-Step Methods | |

Variable Step-Size Multi-Step Methods | |

Extrapolation Methods | |

Higher-Order Equations and Systems of Differential Equations | |

Stability. Stiff Differential Equations | |

Survey of Methods and Software | |

Direct methods for solving linear systems | |

Linear Systems of Equations | |

Pivoting Strategies | |

Linear Algebra and Matrix Inversion | |

The Determinant of a Matrix | |

Matrix Factorization | |

Special Types of Matrices | |

Survey of Methods and Software | |

Iterative techniques in matrix algebra | |

Norms of Vectors and Matrices | |

Eigenvalues and Eigenvectors | |

Iterative Techniques for Solving Linear Systems | |

Error Bounds and Iterative Refinement | |

The Conjugate Gradient Method | |

Survey of Methods and Software | |

Approximation theory | |

Discrete Least Squares Approximation | |

Orthogonal Polynomials and Least Squares Approximation | |

Chebyshev Polynomials and Economization of Power Series | |

Rational Function Approximation | |

Trigonometric Polynomial Approximation | |

Fast Fourier Transforms | |

Survey of Methods and Software | |

Approximating eigenvalues | |

Linear Algebra and Eigenvalues | |

The Power Method | |

Householder's Method | |

The QR Algorithm | |

Survey of Methods and Software | |

Numerical solutions of nonlinear systems of equations | |

Fixed Points for Functions of Several Variables | |

Newton's Method | |

Quasi-Newton Methods | |

Steepest Descent Techniques | |

Homotopy and Continuation Methods | |

Survey of Methods and Software | |

Boundary-value problems for ordinary differential equations | |

The Linear Shooting Method | |

The Shooting Method for Nonlinear Problems | |

Finite-Difference Methods for Linear Problems | |

Finite-Difference Methods for Nonlinear Problems | |

The Rayleigh-Ritz Method | |

Survey of Methods and Software | |

Numerical solutions to partial differential equations | |

Elliptic Partial-Differential Equations | |

Parabolic Partial-Differential Equations | |

Hyperbolic Partial-Differential Equations | |

An Introduction to the Finite-Element Method | |

Survey of Methods and Software | |

Bibliography | |

Answers to Selected Exercises | |

Index | |

Table of Contents provided by Publisher. All Rights Reserved. |