Applied Numerical Methods for Engineers and Scientists

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ISBN: 9780130894809 | 013089480X
Cover: Paperback
Copyright: 9/19/2001

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This comprehensive book includes over 800 problems including open ended, project type and design problems.Chapter topics include Introduction to Numerical Methods; Solution of Nonlinear Equations; Simultaneous Linear Algebraic Equations; Solution of Matrix Eigenvalue Problem; Curve Fitting and Interpolation; Statistical Methods; Numerical Differentiation; Numerical Integration; Numerical Solution of Ordinary Differential Equations: Initial Value Problems; Numerical Solution of Ordinary Differential Equations: Boundary Value Problems; Numerical Solution of Partial Differential Equations; Numerical Methods of Optimization ;Finite Element Method.This book is intended as a reference for numerical methods in engineering.

Preface

xvii

Introduction to Numerical Methods

(47)

Importance of Numerical Methods in Engineering

(1)

Computers

(3)

Computer Programming Languages

(2)

Data Representation

(5)

Programming Structure

(1)

Errors

(9)

Numerical Methods Considered

(8)

Software for Numerical Analysis

(1)

Use of Software Packages

(2)

Computer Programs

(15)

References and Bibliography

(1)

Review Questions

(3)

Problems

(7)

Solution of Nonlinear Equations

(93)

Introduction

(5)

Engineering Applications

(5)

Incremental Search Method

(3)

Bisection Method

(3)

Newton-Raphson Method

(6)

Secant Method

(3)

Regula Falsi Method

(2)

Fixed Point Interation or Successive Substitution Method

(2)

Determination of Multiple Roots

(2)

Bairstow's Method

(5)

Muller's Method

(4)

Newton-Raphson Method for Simultaneous Nonlinear Equations

(4)

Unconstrained Minimization

(1)

Convergence of Methods

(4)

Choice of the Method

(1)

Use of Software Packages

(9)

Computer Programs

107

(34)

References and Bibliography

113

(2)

Review Questions

115

(4)

Problems

119

(22)

Solution of Simultaneous Linear Algebraic Equations

141

(129)

Introduction

142

(1)

Engineering Applications

143

(6)

Vector and Matrix Norms

149

(3)

Basic Concepts of Solution

152

(1)

Linearly Independent Equations

152

(1)

Ill-Conditioned Equations

153

(4)

Graphical Interpretation of the Solution

157

(2)

Solution Using Cramer's Rule

159

(3)

Gauss Elimination Method

162

(7)

Gauss-Jordan Elimination Procedure

169

(3)

LU Decomposition Method

172

(10)

Jacobi Iteration Method

182

(3)

Gauss-Seidel Iteration Method

185

(2)

Relaxation Methods

187

(1)

Simultaneous Linear Equations with Complex Coefficients and Constants

188

(3)

Matrix Inversion

191

(2)

Equations with Special Form of Coefficient Matrix

193

(7)

Overdetermined, Underdetermined, and Homogeneous Equations

200

(9)

Comparative Efficiencies of Various Methods and Recommendations

209

(5)

Choice of the Method

214

(1)

Use of Software Packages

214

(9)

Computer Programs

223

(47)

References and Bibliography

226

(2)

Review Questions

228

(5)

Problems

233

(37)

Solution of Matrix Eigenvalue Problem

270

(94)

Introduction

270

(4)

Engineering Applications

274

(6)

Conversion of General Eigenvalue Problem to Standard Form

280

(5)

Methods of Solving Eigenvalue Problems

285

(1)

Solution of the Characteristic Polynomial Equation

286

(5)

Jacobi Method

291

(6)

Given's Method

297

(4)

Householder's Method

301

(9)

Eigenvalues of a Tridiagonal Matrix

310

(3)

Eigenvectors of a Tridiagonal Matrix

313

(2)

Power Method

315

(9)

Choice of Method

324

(1)

Use of Software Packages

324

(9)

Computer Programs

333

(31)

References and Bibliography

337

(1)

Review Questions

338

(3)

Problems

341

(23)

Curve Fitting and Interpolation

364

(88)

Introduction

364

(2)

Engineering Applications

366

(2)

Collocation-Polynomial Fit

368

(2)

Interpolation

370

(1)

Lagrange Interpolation Formula

370

(3)

Newton's Divided-Difference Interpolating Polynomials

373

(10)

Interpolation Using Chebyshev Polynomials

383

(4)

Interpolation Using Splines

387

(12)

Least-Squares Regression

399

(11)

Curve Fitting with Multiple Variables

410

(2)

Choice of Method

412

(2)

Use of Software Packages

414

(20)

Computer Programs

434

(18)

References and Bibliography

436

(1)

Review Questions

437

(4)

Problems

441

(11)

Statistical Methods

452

(48)

Introduction

452

(1)

Engineering Applications

452

(2)

Basic Definitions

454

(1)

Histogram and Probability Density Function

455

(5)

Statistical Characteristics

460

(4)

Normal Distribution

464

(4)

Statistical Tests

468

(6)

Chi-Square Test for Distribution

474

(2)

Choice of Method

476

(1)

Use of Software Packages

477

(6)

Computer Programs

483

(17)

References and Bibliography

487

(1)

Review Questions

488

(3)

Problems

491

(9)

Numerical Differentiation

500

(60)

Introduction

500

(1)

Engineering Applications

501

(2)

Definition of the Derivative

503

(1)

Basic Finite-Difference Approximations

503

(1)

Using Taylor's Series Expansions

504

(15)

Using Difference Operators

519

(1)

Approximation of Derivatives Using Difference Operators

520

(2)

Using Differentiation of Interpolating Polynomials

522

(3)

Finite-Difference Approximations for Partial Derivatives

525

(4)

Choice of Method

529

(1)

Use of Software Packages

529

(11)

Computer Programs

540

(20)

References and Bibliography

543

(2)

Review Questions

545

(2)

Problems

547

(13)

Numerical Integration

560

(71)

Introduction

560

(2)

Engineering Applications

562

(3)

Newton--Cotes Formulas

565

(9)

Simpson's Rule

574

(9)

General Newton-Cotes Formulas

583

(1)

Richardson's Extrapolation

584

(3)

Romberg Integration

587

(1)

Gauss Quadrature

588

(9)

Integration with Unequal Segments

597

(1)

Numerical Integration of Improper Integrals

598

(4)

Numerical Integration in Two- and Three-Dimensional Domains

602

(3)

Choice of Method

605

(1)

Use of Software Packages

605

(5)

Computer Programs

610

(21)

References and Bibliography

614

(1)

Review Questions

615

(3)

Problems

618

(13)

Ordinary Differential Equations: Initial-Value Problems

631

(92)

Introduction

631

(2)

Engineering Applications

633

(3)

Simultaneous Differential Equations

636

(2)

Solution Concept

638

(1)

Euler's Method

639

(8)

Improvements and Modifications of Euler's Method

647

(7)

Runge-Kutta Methods

654

(11)

Multistep Methods

665

(1)

Adams Methods

665

(7)

Predictor--Corrector Methods

672

(11)

Simultaneous Differential Equations

683

(1)

Stiff Equations

684

(2)

Choice of Method

686

(1)

Use of Software Packages

687

(12)

Computer Programs

699

(24)

References and Bibliography

703

(2)

Review Questions

705

(6)

Problems

711

(12)

Ordinary Differential Equations: Boundary--Value Problems

723

(71)

Introduction

723

(1)

Engineering Applications

724

(3)

Shooting Methods

727

(5)

Generalization to n Equations

732

(8)

Finite-Difference Methods

740

(12)

Solution of Nonlinear Boundary-Value Problems

752

(2)

Solution of Eigenvalue Problems

754

(7)

Choice of Method

761

(1)

Use of Software Packages

762

(15)

Computer Programs

777

(17)

References and Bibliography

781

(1)

Review Questions

782

(3)

Problems

785

(9)

Partial Differential Equations

794

(91)

Introduction

794

(2)

Engineering Applications

796

(3)

Initial and Boundary Conditions

799

(1)

Elliptic Partial Differential Equations

800

(14)

Parabolic Partial Differential Equations

814

(8)

Crank-Nicholson Method

822

(1)

Method of Lines

823

(3)

Two-Dimensional Parabolic Problems

826

(3)

Hyperbolic Partial Differential Equations

829

(11)

Method of Characteristics

840

(6)

Finite-Difference Formulas in Polar Coordinate System

846

(2)

Choice of Method

848

(1)

Use of Software Packages

849

(14)

Computer Programs

863

(22)

References and Bibliography

868

(2)

Review Questions

870

(3)

Problems

873

(12)

Optimization

885

(73)

Introduction

885

(4)

Types of Optimization Problems

889

(1)

Engineering Applications

890

(4)

Optimization Methods from Differential Calculus

894

(8)

Linear-Programming Problem

902

(4)

Simplex Method

906

(1)

Search Methods for Nonlinear Optimization

907

(1)

Optimization of a Function of a Single Variable

908

(10)

Unconstrained Minimization of a Function of Several Variables

918

(6)

Constrained Minimization of a Function of Several Variables

924

(4)

Choice of Method

928

(1)

Use of Software Packages

928

(8)

Computer Programs

936

(22)

References and Bibliography

944

(1)

Review Questions

945

(4)

Problems

949

(9)

Finite-Element Method

958

(61)

Introduction

958

(1)

Engineering Applications

959

(3)

Discretization of the Domain

962

(3)

Interpolation Functions

965

(10)

Derivation of Element Characteristics Matrices and Vectors

975

(6)

Assemblage of Element Characteristic Matrices and Vectors

981

(1)

Solution of System Equations

981

(11)

Choice of Method

992

(1)

Use of Software Packages

993

(8)

Computer Programs

1001

(18)

References and Bibliography

1005

(1)

Review Questions

1006

(4)

Problems

1010

(9)

Appendix A Basics of Fortran 90

1019

(7)

Appendix B Basics of C Language

1026

(4)

Appendix C Basics of Maple

1030

(4)

Appendix D Basics of Matlab

1034

(4)

Appendix E Basics of Mathcad

1038

(4)

Appendix F Review of Matrix Algebra

1042

(7)

Appendix G Statistical Tables

1049

(4)

Index

1053

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Applied Numerical Methods for Engineers and Scientists

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