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Tables of Contents for Numerical Methods
Chapter/Section Title
Page #
Page Count
Mathematical Preliminaries and Error Analysis
1
32
Introduction
1
1
Review of Calculus
1
14
Round-off Error and Computer Arithmetic
15
7
Errors in Scientific Computation
22
7
Computer Software
29
4
Solutions of Equations of One Variable
33
31
Introduction
33
1
The Bisection Method
33
6
The Secant Method
39
6
Newton's Method
45
7
Error Analysis and Accelerating Convergence
52
5
Muller's Method
57
5
Survey of Methods and Software
62
2
Interpolation and Polynomial Approximation
64
47
Introduction
64
2
Lagrange Polynomials
66
11
Divided Differences
77
8
Hermite Interpolation
85
6
Spline Interpolation
91
11
Parametric Curves
102
6
Survey of Methods and Software
108
3
Numerical Integration and Differentiation
111
68
Introduction
111
1
112
8
120
9
Romberg Integration
129
9
138
5
143
7
Multiple Integrals
150
11
Improper Integrals
161
6
Numerical Differentiation
167
10
Survey of Methods and Software
177
2
Numerical Solution of Initial-Value Problems
179
62
Introduction
179
3
Taylor Methods
182
11
Runge-Kutta Methods
193
8
Predictor-Corrector Methods
201
8
Extrapolation Methods
209
5
214
9
Methods for Systems of Equations
223
11
Stiff Differential Equations
234
5
Survey of Methods and Software
239
2
Direct Methods for Solving Linear Systems
241
49
Introduction
241
1
Gaussian Elimination
241
11
Pivoting Strategies
252
8
Linear Algebra and Matrix Inversion
260
12
Matrix Factorization
272
6
Techniques for Special Matrices
278
9
Survey of Methods and Software
287
3
Iterative Methods for Solving Linear Systems
290
50
Introduction
290
1
Convergence of Vectors
291
8
Eigenvalues and Eigenvectors
299
7
The Jacobi and Gauss-Seidel Methods
306
6
The SOR Method
312
6
Error Bounds and Iterative Refinement
318
7
325
13
Survey of Methods and Software
338
2
Approximation Theory
340
42
Introduction
340
1
Discrete Least Squares Approximation
340
9
Continuous Least Squares Approximation
349
8
Chebyshev Polynomials
357
6
Rational Function Approximation
363
6
Trigonometric Polynomial Approximation
369
6
Fast Fourier Transforms
375
5
Survey of Methods and Software
380
2
Approximating Eigenvalues
382
34
Introduction
382
1
Isolating Eigenvalues
382
6
The Power Method
388
13
Householder's Method
401
5
The QR Method
406
8
Survey of Methods and Software
414
2
Solutions of Systems of Nonlinear Equations
416
34
Introduction
416
3
Newton's Method for Systems
419
9
Quasi-Newton Methods
428
7
The Steepest Descent Method
435
5
Homotopy and Continuation Methods
440
8
Survey of Methods and Software
448
2
Boundary-Value Problems for Ordinary Differential Equations
450
41
Introduction
450
1
The Linear Shooting Method
451
5
Linear Finite-Difference Methods
456
7
The Nonlinear Shooting Method
463
6
Nonlinear Finite-Difference Methods
469
5
Variational Techniques
474
14
Survey of Methods and Software
488
3
Numerical Methods for Partial-Differential Equations
491
48
Introduction
491
2
Finite-Difference Methods for Elliptic Problems
493
8
Finite-Difference Methods for Parabolic Problems
501
13
Finite-Difference Methods for Hyperbolic Problems
514
8
Introduction to the Finite-Element Method
522
15
Survey of Methods and Software
537
2
Bibliography
539
6