Mathematical Preliminaries and Error Analysis | |

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 | |

Newton's Method and its Extensions | |

Error Analysis for Iterative Methods | |

Accelerating Convergence | |

Zeros of Polynomials and M?ller's Method | |

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Interpolation and Polynomial Approximation | |

Interpolation and the Lagrange Polynomial | |

Data Approximation and Neville's Method | |

Divided Differences | |

Hermite Interpolation | |

Cubic Spline Interpolation | |

Parametric Curves | |

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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 | |

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Intial-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 | |

Multistep Methods | |

Variable Step-Size Multistep Methods | |

Extrapolation Methods | |

Higher-Order Equations and Systems of Differential Equations | |

Stability | |

Stiff Differential Equations | |

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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 | |

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Iterative Techniques in Matrix Algebra | |

Norms of Vectors and Matrices | |

Eigenvalues and Eigenvectors | |

The Jacobi and Gauss-Siedel Iterative Techniques | |

Iterative Techniques for Solving Linear Systems | |

Relaxation Techniques for Solving Linear Systems | |

Error Bounds and Iterative Refinement | |

The Conjugate Gradient Method | |

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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 | |

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Approximating Eigenvalues | |

Linear Algebra and Eigenvalues | |

Orthogonal Matrices and Similarity Transformations | |

The Power Method | |

Householder's Method | |

The QR Algorithm | |

Singular Value Decomposition | |

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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 | |

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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 | |

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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 | |

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