| |
| |
| |
| Preliminaries | |
| |
| |
| Analysis versus Numerical Analysis | |
| |
| |
| Computers and Numerical Analysis | |
| |
| |
| An Illustrative Example | |
| |
| |
| Kinds of Errors in Numerical Procedures | |
| |
| |
| Interval Arithmetic | |
| |
| |
| Parallel and Distributed Computing | |
| |
| |
| Measuring the Efficiency of Procedures | |
| |
| |
| |
| Solving Nonlinear Equations | |
| |
| |
| Interval Halving (Bisection) | |
| |
| |
| Linear Interpolation Methods | |
| |
| |
| Newton's Method | |
| |
| |
| Muller's Method | |
| |
| |
| Fixed-Point Iteration | |
| |
| |
| Other Methods | |
| |
| |
| Nonlinear Systems | |
| |
| |
| |
| Solving Sets of Equations | |
| |
| |
| Matrices and Vectors | |
| |
| |
| Elimination Methods | |
| |
| |
| The Inverse of a Matrix and Matrix Pathology | |
| |
| |
| Almost Singular Matrices - Condition Numbers | |
| |
| |
| Interactive Methods | |
| |
| |
| Parallel Processing | |
| |
| |
| |
| Interpolation and Curve Fitting | |
| |
| |
| Interpolating Polynomials | |
| |
| |
| Divided Differences | |
| |
| |
| Spline Curves | |
| |
| |
| Bezier Curves and B-Splines | |
| |
| |
| Interpolating on a Surface | |
| |
| |
| Least Squares Approximations | |
| |
| |
| |
| Approximation of Functions | |
| |
| |
| Chebyshev Polynomials and Chebyshev Series | |
| |
| |
| Rational Function Approximations | |
| |
| |
| Fourier Series | |
| |
| |
| |
| Numerical Differentiation and Integration | |
| |
| |
| Differentiation with a Computer | |
| |
| |
| Numerical Integration - The Trapezoidal Rule | |
| |
| |
| Simpson's Rules | |
| |
| |
| An Application of Numerical Integration - Fourier Series and Fourier Transforms Adaptive Integration | |
| |
| |
| Gaussian Quadrature | |
| |
| |
| Multiple Integrals | |
| |
| |
| Applications of Cubic Splines | |
| |
| |
| |
| Numerical Solution of Ordinary Differential Equations | |
| |
| |
| The Taylor Series Method | |
| |
| |
| The Euler Method and Its Modification | |
| |
| |
| Runge-Kutta Methods | |
| |
| |
| Multistep Methods | |
| |
| |
| Higher-Order Equations and Systems | |
| |
| |
| Stiff Equations | |
| |
| |
| Boundary-Value Problems | |
| |
| |
| Characteristic-Value Problems | |
| |
| |
| |
| Optimization | |
| |
| |
| Finding the Minimum of y = f(x) | |
| |
| |
| Minimizing a Function of Several Variables | |
| |
| |
| Linear Programming | |
| |
| |
| Nonlinear Programming | |
| |
| |
| Other Optimizations | |
| |
| |
| |
| Partial Differential Equations | |
| |
| |
| Elliptic Equations | |
| |
| |
| Parabolic Equations | |
| |
| |
| Hyperbolic Equations | |
| |
| |
| |
| Finite Element Analysis | |
| |
| |
| Mathematical Background | |
| |
| |
| Finite Elements for Ordinary Differential Equation | |
| |
| |
| Finite Elements for Partial Differential Equation | |
| |
| |
| Appendices | |
| |
| |
| |
| Some Basic Information from Calculus | |
| |
| |
| |
| Software Resources | |
| |
| |
| Answers to Selected Exercises | |
| |
| |
| References | |
| |
| |
| Index | |
