Engineering Analysis: Interactive Methods and

This book provides a concise introduction to numerical concepts in engineering analysis, using FORTRAN, QuickBASIC, MATLAB, and Mathematica to illustrate the examples. Discussions include:o matrix algebra and analysiso solution of matrix equationso methods of curve fito methods for finding the roots of polynomials and transcendental equationso finite differences and methods for interpolation and numerical differentiationo numerical computation of single and double integralso numerical solution of ordinary differential equationsEngineering Analysis:o teaches readers to become proficient in FORTRAN or QuickBASIC programming to solve engineering problemso provides an introduction to MATLAB and Mathematica, enabling readers to write supplementary m-files for MATLAB and toolkits for Mathematica using C-like commandsThe book emphasizes interactive operation in developing computer programs throughout, enabling the values of the parameters involved in the problem to be entered by the user of the program via a keyboard.In introducing each numerical method, Engineering Analysis gives minimum mathematical derivations but provides a thorough explanation of computational procedures to solve a specific problem. It serves as an exceptional text for self-study as well as resource for general reference.

1 Matrix Algebra and Solution of Matrix Equations

1

(64)

1.1 Introduction

1

(1)

1.2 Manipulation of Matrices

2

(23)

1.3 Solution of Matrix Equation

25

(5)

1.4 Program Gauss -- Gaussian Elimination Method

30

(11)

1.5 Matrix Inversion, Determinant, and Program MatxInvD

41

(13)

1.6 Problems

54

(9)

1.7 Reference

63

(2)

2 Exact, Least-Squares, and Spline Curve-Fits

65

(42)

2.1 Introduction

65

(1)

2.2 Exact Curve Fit

65

(6)

2.3 Program LeastSq1 -- Linear Least-Squares Curve-Fit

71

2.4 Program LeastSqG -- Generalized Least-Squares Curve-Fit

70

2.5 Program CubeSpln -- Curve Fitting with Cubic Spline

88

(12)

2.6 Problems

100

(5)

2.7 Reference

105

(2)

3 Roots of Polynomial and Transcendental Equations

107

(36)

3.1 Introduction

107

(1)

3.2 Iterative Methods and Program Roots

108

(10)

3.3 Program NewRaphG -- Generalized Newton-Raphson Iterative Method

118

(9)

3.4 Program Bairstow -- Bairstow Method for Finding Polynomial Roots

127

(9)

3.5 Problems

136

(5)

3.6 References

141

(2)

4 Finite Differences, Interpolation, and Numerical Differentiation

143

(28)

4.1 Introduction

143

(1)

4.2 Finite Differences and Program DiffTabl -- Constructing Difference Table

144

(17)

4.3 Program LagrangI -- Applications of Lagrangian Interpolation Formula

161

(7)

4.4 Problems

168

(2)

4.5 Reference

170

(1)

5 Numerical Integration and Program Volume

171

(30)

5.1 Introduction

171

(3)

5.2 Program NuIntGra -- Numerical Integration by Application of the Trapezoidal and Simpson Rules

174

(12)

5.3 Program Volume -- Numerical Solution of Double Integral

186

(11)

5.4 Problems

197

(3)

5.5 References

200

(1)

6 Ordinary Differential Equations -- Initial and Boundary Value Problems

201

(56)

6.1 Introduction

201

(1)

6.2 Program RungeKut -- Application of Runge-Kutta Method for Solving InitialValue Problems

202

(21)

6.3 Program OdeBvpRK -- Application of Runge-Kutta Method for Solving Boundary Value Problems

223

(11)

6.4 Program OdeBvpFD -- Application of Finite-Difference Method for Solving Boundary-Value Problems

234

(13)

6.5 Problems

247

(9)

6.6 References

256

(1)

7 Eigenvalue and Eigenvector Problems

257

(44)

7.1 Introduction

257

(3)

7.2 Programs EigenODE.Stb and EigenODE.Vib -- for Solving Stability and Vibration Problems

260

(7)

7.3 Program CharacEq -- Derivation of Characteristic Equation of a Specified Square Matrix

267

(8)

7.4 Program Eigen Vec -- Solving Eigenvector by Gaussian Elimination Method

275

(10)

7.5 Program EigenvIt -- Iterative Solution of Eigenvalue and Eigenvector

285

(9)

7.6 Problems

294

(6)

7.7 References

300

(1)

8 Partial Differential Equations

301

(48)

8.1 Introduction

301

(1)

8.2 Program ParabPDE -- Numerical Solution of Parabolic Partial Differential Equations

302

(9)

8.3 Program Relaxatn -- Solving Elliptical Partial Differential Equations by Relaxation Method

311

(21)

8.4 Program WavePDE -- Numerical Solution of Wave Problems Governed by Hyperbolic Partial Differential Equations

332

(10)

8.5 Problems

342

(5)

8.6 References

347

(2)

General Index

349

(4)

FORTRAN Commands and Programs Index

353

(2)

QuickBASIC Commands and Programs Index

355

(2)

MATLAB Commands and Programs Index

357

(2)

Mathematica Commands and Programs Index

359

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Engineering Analysis: Interactive Methods and Programs with FORTRAN, QuickBASIC, MATLAB, and Mathematica

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Table of Contents

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Engineering Analysis: Interactive Methods and Programs with FORTRAN, QuickBASIC, MATLAB, and Mathematica

Summary

Table of Contents

Supplemental Materials

Digital License