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Numerical Methods

by Faires, J. Douglas

Edition:

2nd

ISBN13:

9780534351878

ISBN10:

0534351875

Format:

Paperback

Pub. Date:

3/26/1998

Publisher(s):

Brooks Cole

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Summary

Solutions to odd-numbered exercises in the text.

Preface

Chapter 1 Mathematical Preliminaries and Error Analysis

(29)

1.1 Introduction

(1)

1.2 Review of Calculus

(13)

1.3 Round-off Error and Computer Arithmetic

(6)

1.4 Errors in Scientific Computation

(8)

1.5 Computer Software

(2)

Chapter 2 Solutions of Equations of One Variable

(30)

2.1 Introduction

(1)

2.2 The Bisection Method

(5)

2.3 The Secant Method

(7)

2.4 Newton's Method

(7)

2.5 Error Analysis and Accelerating Convergence

(4)

2.6 Muller's Method

(6)

2.7 Survey of Methods and Software

(1)

Chapter 3 Interpolation and Polynomial Approximation

(47)

3.1 Introduction

(2)

3.2 Lagrange Polynomials

(12)

3.3 Divided Differences

(8)

3.4 Hermite Interpolation

(5)

3.5 Spline Interpolation

(12)

3.6 Parametric Curves

(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

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Numerical Methods

9780534351878

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Summary

Table of Contents