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Numerical Methods

ISBN: 9780534351878 | 0534351875
Edition: 2nd
Format: Paperback
Publisher: Brooks Cole
Pub. Date: 3/26/1998

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SummaryTable of Contents
Solutions to odd-numbered exercises in the text.
Prefaceix
Chapter 1 Mathematical Preliminaries and Error Analysis
1(29)
1.1 Introduction
1(1)
... MORE
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)
Bibliography519(6)
Answers for Numerical Methods525(62)
Index587

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