search for books and compare prices
Tables of Contents for Numerical Methods
Chapter/Section Title
Page #
Page Count
Preface
ix
Chapter 1 Mathematical Preliminaries and Error Analysis
1
29
1.1 Introduction
1
1
1.2 Review of Calculus
1
13
1.3 Round-off Error and Computer Arithmetic
14
6
1.4 Errors in Scientific Computation
20
8
1.5 Computer Software
28
2
Chapter 2 Solutions of Equations of One Variable
30
30
2.1 Introduction
30
1
2.2 The Bisection Method
30
5
2.3 The Secant Method
35
7
2.4 Newton's Method
42
7
2.5 Error Analysis and Accelerating Convergence
49
4
2.6 Muller's Method
53
6
2.7 Survey of Methods and Software
59
1
Chapter 3 Interpolation and Polynomial Approximation
60
47
3.1 Introduction
60
2
3.2 Lagrange Polynomials
62
12
3.3 Divided Differences
74
8
3.4 Hermite Interpolation
82
5
3.5 Spline Interpolation
87
12
3.6 Parametric Curves
99
6
3.7 Survey of Methods and Software
105
2
Chapter 4 Numerical Integration and Differentiation
107
69
4.1 Introduction
107
1
4.2 Basic Quadrature Rules
107
9
4.3 Composite Quadrature Rules
116
10
4.4 Romberg Integration
126
8
4.5 Gaussian Quadrature
134
6
4.6 Adaptive Quadrature
140
7
4.7 Multiple Integrals
147
10
4.8 Improper Integrals
157
6
4.9 Numerical Differentiation
163
11
4.10 Survey of Methods and Software
174
2
Chapter 5 Numerical Solution of Initial-Value Problems
176
61
5.1 Introduction
176
3
5.2 Taylor Methods
179
11
5.3 Runge-Kutta Methods
190
8
5.4 Predictor-Corrector Methods
198
8
5.5 Extrapolation Methods
206
5
5.6 Adaptive Techniques
211
9
5.7 Methods for Systems of Equations
220
10
5.8 Stiff Differential Equations
230
5
5.9 Survey of Methods and Software
235
2
Chapter 6 Direct Methods for Solving Linear Systems
237
50
6.1 Introduction
237
1
6.2 Gaussian Elimination
237
11
6.3 Pivoting Strategies
248
8
6.4 Linear Algebra and Matrix Inversion
256
12
6.5 Matrix Factorization
268
7
6.6 Techniques for Special Matrices
275
9
6.7 Survey of Methods and Software
284
3
Chapter 7 Iterative Methods for Solving Linear Systems
287
36
7.1 Introduction
287
1
7.2 Convergence of Vectors
288
8
7.3 Eigenvalues and Eigenvectors
296
7
7.4 The Jacobi and Gauss-Seidel Methods
303
6
7.5 The SOR Method
309
5
7.6 Error Bounds and Iterative Refinement
314
8
7.7 Survey of Methods and Software
322
1
Chapter 8 Approximation Theory
323
43
8.1 Introduction
323
1
8.2 Discrete Least Squares Approximation
323
9
8.3 Continuous Least Squares Approximation
332
8
8.4 Chebyshev Polynomials
340
6
8.5 Rational Function Approximation
346
6
8.6 Trigonometric Polynomial Approximation
352
7
8.7 Fast Fourier Transforms
359
5
8.8 Survey of Methods and Software
364
2
Chapter 9 Approximating Eigenvalues
366
33
9.1 Introduction
366
1
9.2 Isolating Eigenvalues
366
6
9.3 The Power Method
372
13
9.4 Householder's Method
385
5
9.5 The QR Method
390
7
9.6 Survey of Methods and Software
397
2
Chapter 10 Solutions of Systems of Nonlinear Equations
399
26
10.1 Introduction
399
3
10.2 Newton's Methods for Systems
402
8
10.3 Quasi-Newton Methods
410
7
10.4 The Steepest Descent Method
417
6
10.5 Survey of Methods and Software
423
2
Chapter 11 Boundary-Value Problems for Ordinary Differential Equations
425
42
11.1 Introduction
425
1
11.2 The Linear Shooting Methods
426
6
11.3 Linear Finite Difference Methods
432
7
11.4 The Nonlinear Shooting Method
439
7
11.5 Nonlinear Finite-Difference Methods
446
4
11.6 Variational Techniques
450
15
11.7 Survey of Methods and Software
465
2
Chapter 12 Numerical Methods for Partial-Differential Equations
467
52
12.1 Introduction
467
3
12.2 Finite-Difference Methods for Elliptic Problems
470
8
12.3 Finite-Difference Methods for Parabolic Problems
478
14
12.4 Finite-Difference Methods for Hyperbolic Problems
492
9
12.5 Introduction to the Finite-Element Method
501
15
12.6 Survey of Methods and Software
516
3
Bibliography
519
6
Answers for Numerical Methods
525
62
Index
587