Mathematical Preliminaries | p. 1 |

Review of Calculus | p. 2 |

Roundoff Errors and Computer Arithmetic | p. 18 |

Algorithms and Convergence | p. 31 |

Numerical Software | p. 40 |

Solutions of Equations in One Variable | p. 47 |

The Bisection Method | p. 48 |

Fixed-Point Iteration | p. 55 |

Newton's Method | p. 66 |

Error Analysis for Iterative Methods | p. 78 |

Accelerating Convergence | p. 86 |

Zeros of Polynomials and Muller's Method | p. 91 |

Survey of Methods and Software | p. 101 |

Interpolation and Polynomial Approximation | p. 104 |

Interpolation and the Lagrange Polynomial | p. 107 |

Divided Differences | p. 122 |

Hermite Interpolation | p. 133 |

Cubic Spline Interpolation | p. 141 |

Parametric Curves | p. 156 |

Survey of Methods and Software | p. 163 |

Numerical Differentiation and Integration | p. 166 |

Numerical Differentiation | p. 167 |

Richardson's Extrapolation | p. 178 |

Elements of Numerical Integration | p. 186 |

Composite Numerical Integration | p. 196 |

Romberg Integration | p. 207 |

Adaptive Quadrature Methods | p. 213 |

Gaussian Quadrature | p. 220 |

Multiple Integrals | p. 227 |

Improper Integrals | p. 241 |

Survey of Methods and Software | p. 247 |

Initial-Value Problems for Ordinary Differential Equations | p. 249 |

The Elementary Theory of Initial-Value Problems | p. 251 |

Euler's Method | p. 256 |

Higher-Order Taylor Methods | p. 266 |

Runge-Kutta Methods | p. 272 |

Error Control and the Runge-Kutta-Fehlberg Method | p. 282 |

Multistep Methods | p. 289 |

Variable Step-Size Multistep Methods | p. 301 |

Extrapolation Methods | p. 307 |

Higher-Order Equations and Systems of Differential Equations | p. 313 |

Stability | p. 324 |

Stiff Differential Equations | p. 334 |

Survey of Methods and Software | p. 342 |

Direct Methods for Solving Linear Systems | p. 344 |

Linear Systems of Equations | p. 345 |

Pivoting Strategies | p. 359 |

Linear Algebra and Matrix Inversion | p. 370 |

The Determinant of a Matrix | p. 383 |

Matrix Factorization | p. 388 |

Special Types of Matrices | p. 398 |

Survey of Methods and Software | p. 413 |

Iterative Techniques in Matrix Algebra | p. 417 |

Norms of Vectors and Matrices | p. 418 |

Eigenvalues and Eigenvectors | p. 430 |

Iterative Techniques for Solving Linear Systems | p. 437 |

Error Bounds and Iterative Refinement | p. 454 |

The Conjugate Gradient Method | p. 465 |

Survey of Methods and Software | p. 481 |

Approximation Theory | p. 483 |

Discrete Least Squares Approximation | p. 484 |

Orthogonal Polynomials and Least Squares Approximation | p. 498 |

Chebyshev Polynomials and Economization of Power Series | p. 507 |

Rational Function Approximation | p. 517 |

Trigonometric Polynomial Approximation | p. 529 |

Fast Fourier Transforms | p. 537 |

Survey of Methods and Software | p. 548 |

Approximating Eigenvalues | p. 550 |

Linear Algebra and Eigenvalues | p. 551 |

The Power Method | p. 560 |

Householder's Method | p. 577 |

The QR Algorithm | p. 585 |

Survey of Methods and Software | p. 597 |

Numerical Solutions of Nonlinear Systems of Equations | p. 600 |

Fixed Points for Functions of Several Variables | p. 602 |

Newton's Method | p. 611 |

Quasi-Newton Methods | p. 620 |

Steepest Descent Techniques | p. 628 |

Homotopy and Continuation Methods | p. 635 |

Survey of Methods and Software | p. 643 |

Boundary-Value Problems for Ordinary Differential Equations | p. 645 |

The Linear Shooting Method | p. 646 |

The Shooting Method for Nonlinear Problems | p. 653 |

Finite-Difference Methods for Linear Problems | p. 660 |

Finite-Difference Methods for Nonlinear Problems | p. 667 |

The Rayleigh-Ritz Method | p. 672 |

Survey of Methods and Software | p. 688 |

Numerical Solutions to Partial Differential Equations | p. 691 |

Elliptic Partial Differential Equations | p. 694 |

Parabolic Partial Differential Equations | p. 704 |

Hyperbolic Partial Differential Equations | p. 718 |

An Introduction to the Finite-Element Method | p. 726 |

Survey of Methods and Software | p. 741 |

Bibliography | p. 743 |

Answers to Selected Exercises | p. 753 |

Index | p. 831 |

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