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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 | |
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Interpolation and polynomial approximation | |
Interpolation and the LaGrange Polynomial | |
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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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 | |
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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 | |
Iterative 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 | |
The Power Method | |
Householder's Method | |
The QR Algorithm | |
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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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Bibliography | |
Answers to Selected Exercises | |
Index | |
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