| |
| |
| |
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 | |