PrefaceContents1 Mathematical Preliminaries1.1 Review of Calculus1.2 Roundoff Errors and Computer Arithmetic1.3 Algorithms and Convergence1.4 Numerical Software2 Solutions of Equations in One Variable2.1 The Bisection Method2.2 Fixed-Point Iteration2.3 Newton s Method2.4 Error Analysis for Iterative Methods2.5 Accelerating Convergence2.6 Zeros of Polynomials and Mller s Method2.7 Survey of Methods and Software3 Interpolation and Polynomial Approximation3.1 Interpolation and the Lagrange Polynomial3.2 Divided Differences3.3 Hermite Interpolation3.4 Cubic Spline Interpolation3.5 Parametric Curves3.6 Survey of Methods and Software4 Numerical Differentiation and Integration4.1 Numerical Differentiation4.2 Richardson s Extrapolation4.3 Elements of Numerical Integration4.4 Composite Numerical Integration4.5 Romberg Integration4.6 Adaptive Quadrature Methods4.7 Gaussian Quadrature4.8 Multiple Integrals4.9 Improper Integrals4.10 Survey of Methods and software5 Initial-Value Problems for Ordinary Differential Equations5.1 The Elementary Theory of Initial-Value Problems5.2 Euler s Method5.3 Higher-Order Taylor Methods5.4 Runge-Kutta Methods5.5 Error Control and the Runge-Kutta-Fehlberg Method5.6 Multistep Methods5.7 Variable Step-Size Multistep Methods5.8 Extrapolation Methods5.9 Higher-Order Equations and Systems of Differential Equations5.10 Stability5.11 Stiff Differential Equations5.12 Survey of Methods and Software6 Direct Methods for Solving Linear Systems6.1 Linear Systems of Equations6.2 Pivoting Strategies6.3 Linear Algebra and Matrix Inversion6.4 The Determinant of a Matrix6.5 Matrix Factorization6.6 Special Types of Matrices6.7 Survey of Methods and Software7 Iterative Techniques in Matrix Algebra7.1 Norms of Vectors and Matrices7.2 Eigenvalues and Eigenvectors7.3 Iterative Techniques for Solving Linear Systems7.4 Error Bounds and Iterative Refinement7.5 The Conjugate Gradient Method7.6 Survey of Methods and Software8 Approximation Theory8.1 Discrete Least Squares Approximation8.2 Orthogonal Polynomials and Least Squares Approximation8.3 Chebyshev Polynomials and Economization of power Series8.4 Rational Function Approximation8.5 Trigonometric Polynomial Approximation8.6 Fast Fourier Transforms8.7 survey of Methods and software9 Approximating Eigenvalues9.1 Linear Algebra and Eigenvalues9.2 The Power Method9.3 Householder s Method9.4 The QR Algorithm9.5 Survey of Methods and Software10 Numerical Solutions of Nonlinear Systems of Equations10.1 Fixed Points for Functions of Several Variables10.2 Newton s Method10.3 Quasi-Newton Methods10.4 Steepest Descent Techniques10.5 Homotopy and Continuation Methods10.6 Survey of Methods and software11 Boundary-Value Problems for Ordinary Differential Equations11.1 The Linear Shooting Method11.2 The Shooting Method for Nonlinear Problems11.3 Finite-Difference Methods for Linear Problems11.4 Finite-Difference Methods for Nonlinear Problems11.5 The Rayleigh-Ritz Method11.6 Survey of Methods and Software12 Numerical Solutions to partial Differential Equations12.1 Elliptic Partial Differential Equations12.2 Parabolic Partial Differential Equations12.3 Hyperbolic Partial Differential Equations12.4 An Introduction to the Finite-Element Method12.5 Survey of Methods and SoftwareBibliographyAnswers to Selected ExercisesIndex