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

This book provides a concise introduction to the numerical concepts in engineering analysis, using FORTRAN, QuickBASIC, MATLAB, and Mathematica to illustrate the examples. Discussions include matrix algebra and analysis, solution of matrix equations, methods of curve fits, methods for finding the roots of polynomials and transcendental equations, finite differences and methods for interpolation and numerical differentiation, numerical computation of single and double integrals, and numerical solution of ordinary differential equations. TOC.PDF -1 Engineering Analysis 1 Engineering Analysis 1 Files Available from CRC Press 3 Dedication 6 Preface and Acknowledgments 7 Contents 9 CH-01.PDF 1 Engineering Analysis 11 Table of Contents -1 Matrix Algebra and Solution of Matrix Equations 11 1.1 Introduction 11 1.2 Manipulation of Matrices 12 1.2 Multiplication of Matrices 14 FORTRAN Version 16 Interactive Operation 18 More Programming Review 20 Sample Applications 26 QuickBASIC Version 28 Sample Applications 30 MATLAB Applications 32 Mathematica Applications 34 1.3 Solution of Matrix Equation 35 QuickBASIC Version of the program CramerR 38 1.4 Program Gauss 40 Gaussian Elimination Method 40 QuickBASIC Version 44 Sample Application 44 FORTRAN Version 45 Sample Application 46 Gauss-Jordan Method 46 QuickBASIC Version 47 FORTRAN Version 48 Sample Applications 49 MATLAB Applications 49 Mathematica Applications 50 1.5 Matrix Inversion, Determinant, and Program MatxInvD 51 QuickBASIC Version 52 Sample Application 53 FORTRAN Version 53 Sample Applications 55 MATLAB Application 55 Mathematica Applications 56 Transformation of Coordinate Systems, Rotation, and Animation 57 Function Animate1(Ncycle,Damping) 61 QuickBASIC Version 62 1.6 Problems 64 Matrix Algebra 64 Gauss 66 Matrix Inversion 67 1.7 Reference 73 CH-02.PDF 1 Engineering Analysis 74 Table of Contents -1 Exact, Least-Squares, and Cubic Spline Curve-Fits 74 2.1 Introduction 74 2.2 Exact Curve Fit 74 FORTRAN Version 75 Sample Applications 76 QuickBASIC Version 77 Sample Application 77 MATLAB Application 77 2.3 Program LeastSq1—Least-Squares Linear Curve-Fit 80 QuickBASIC Version 82 Sample Application 83 FORTRAN Version 83 Sample Application 84 MATLAB Application 84 Transformed Least-Squares Curve-Fit 84 2.4 Program LeastSqG — Generalized Least-Squares CurveFit 87 QuickBASIC Version 89 Sample Applications 90 FORTRAN Version 91 Sample Application 92 MATLAB Application 92 Mathematica Applications 96 2.5 Program CubeSpln — Curve Fitting with Cubic Spline 97 QuickBASIC Version 100 Sample Application 102 MATLAB Application 102 Mathematica Applications 105 2.6 Problems 109 Exact Curve-Fit 109 LeastSq1 109 LEASTSQG 110 Cubic Spline 112 2.7 References 114 CH-03.PDF 1 Engineering Analysis 115 Table of Contents -1 Roots of Polynomials and Transcendental Equations 115 3.1 Introduction 115 3.2 Iterative Methods and Program FindRoot 116 Incremental Search 116 Bisection Search 117 Linear Interpolation 118 Newton-Raphson Iterative Method 118 QuickBASIC Version 119 Sample Application 119 FORTRAN Version 120 Sample Application 121 MATLAB Application 122 Method of Successive Substitution 124 Mathematica Applications 125 3.3 Program NewRaphG— Generalized Newton-Raphson Iterative Method 126 Transcendental Equations 127 Extended Newton-Raphson Method 130 QuickBASIC Version 131 FORTRAN Version 131 Sample Application 132 MATLAB Applications 132 Mathematica Applications 134 3.4 Program Bairstow — Bairstow’s Method for Finding Polynomial Roots 135 QuickBASIC Version 138 Sample Application 139 FORTRAN Version 139 Sample Application 141 MATLAB Application 141 Mathematica Applications 142 3.5 Problems 144 FindRoot 144 NewRaphG 146 Bairstow 148 3.6 References 149 CH-04.PDF 1 Engineering Analysis 150 Table of Contents -1 Finite Differences, Interpolation, and Numerical Differentiation 150 4.1 Introduction 150 4.2 Program DiffTabl — Applications of Finite-Difference Table 151 Backward-Difference Operator 153 Central-Difference Operator 154 Differentiation Operator 155 QuickBASIC Version 157 Sample Application 158 FORTRAN Version 158 Sample Application 161 MATLAB Application 161 Mathematica Applications 164 4.3 Program LagrangI — Applications of Lagrangian Interpolation Formula 168 QuickBASIC Version 170 Sample Application 171 FORTRAN Version 171 Sample Application 172 MATLAB Application 172 Mathematica Applications 174 4.4 Problems 175 DiffTabl 175 LagrangI 176 4.5 Reference 177 CH-05.PDF 1 Engineering Analysis 178 Table of Contents -1 Numerical Integration and Program Volume 178 5.1 Introduction 178 5.2 Program NuIntGra — Numerical Integration by Application of the Trapezoidal and Simpson Rules 181 Trapezoidal Rule 185 Simpson’s Rule 186 QuickBASIC Version 190 FORTRAN Version 191 MATLAB Application 192 Mathematica Application 193 5.3 Program Volume — Numerical Approximation of Double Integration 193 FORTRAN Version 197 Sample Application 199 QuickBASIC Version 199 Sample Applications 200 MATLAB Application 200 Mathematica Applications 202 5.4 Problems 204 NuIntGra 204 Volume 205 5.5 References 207 CH-06.PDF 1 Engineering Analysis 208 Table of Contents -1 Ordinary Differential Equations— Initial and Boundary Value Problems 208 6.1 Introduction 208 6.2 Program RungeKut — Application of the Runge-Kutta Method for Solving the Initial-Value Problems 209 Runge-Kutta Method (Fourth-Order) 211 Subroutine RKN 214 FORTRAN Version 214 QuickBASIC Version 215 Program RungeKut 215 QuickBASIC Version 216 FORTRAN Version 216 Function F 217 QuickBASIC Version 217 FORTRAN Version 218 Sample Applications of the program RungeKut 219 A Nonlinear Oscillation Problem Solved by RungeKut 221 MATLAB Application 224 Mathematica Applications 228 6.3 Program OdeBvpRK — Application of Runge-Kutta Method for Solving Boundary-Value Problems 230 Numerical Examples 232 FORTRAN Version 234 QuickBASIC Version 236 MATLAB Applications 236 Mathematica Applications 238 6.4 Program OdeBvpFD — Application of Finite Difference Method for Solving Boundary-Value Problems 241 FORTRAN Version 247 Sample Application 247 QuickBASIC Version 248 Sample Applications 249 MATLAB Applications 250 Membrane Problem 250 Beam Deflection Problem 252 Mathematica Applications 253 6.5 Problems 254 RungeKut 254 OdeBvpRK 259 OdeBvpFD 261 6.6 References 263 Ch-07.pdf 1 Engineering Analysis 264 Table of Contents -1 Eigenvalue and Eigenvector Problems 264 7.1 Introduction 264 7.2 Programs EigenODE.Stb and EigenODE.Vib — for Solving Stability and Vibration Problems 267 Program EigenODE.Stb 268 FORTRAN Version 268 Sample Applications 269 Program EigenODE.Vib 270 FORTRAN Version 271 Sample Application 271 MATLAB Applications 272 Mathematica Applications 274 7.3 Program CharacEq — Derivation of Characteristic Equationof a Specified Square Matrix 274 QuickBASIC Version 276 Sample Application 277 FORTRAN Version 277 Sample Application 278 MATLAB Application 279 Mathematica Applications 280 7.4 Program EigenVec — Solving Eigenvector by Gaussian Elimination Method 282 QuickBASIC Version 283 Sample Application 284 FORTRAN Version 284 Sample Application 285 MATLAB Applications 286 Mathematica Applications 286 Principal Stresses and Planes 287 Quadratic Forms and Canonical Transformation 290 7.5 Program EigenvIt — Iterative Solution of the Eigenvalue and Eigenvector 292 QuickBASIC Version 293 Sample Application 294 FORTRAN Version 294 MATLAB Application 295 Mathematica Applications 299 7.6 Problems 301 Programs EigenODE.Stb and EigenODE.Vib 301 CharacEq 301 EigenVec 303 EigenvIt 304 7.7 References 307 CH-08.PDF 1 Engineering Analysis 308 Table of Contents -1 Partial Differential Equations 308 8.1 Introduction 308 8.2 Program ParabPDE — Numerical Solution of Parabolic Partial Differential Equations 309 FORTRAN Version 311 Sample Output 312 QuickBASIC Version 313 MATLAB Applications 313 Mathematica Applications 315 8.3 Program Relaxatn — Solving Elliptical Partial Differential Equations by Relaxation Method 318 FORTRAN Version 322 Sample Results 323 QuickBASIC Version 325 Sample Results 326 Irregular Boundaries 326 MATLAB Application 327 Mathematica Applications 333 Warping Analysis of a Twisted Bar with Noncircular Cross Section 334 8.4 Program WavePDE — Numerical Solution of Wave Problems Governed by Hyperbolic Partial Differential Equations 339 QuickBASIC Version 341 Sample Application 342 MATLAB Applications 344 Mathematica Application 346 8.5 Problems 349 ParabPDE 349 Relaxatn 349 WavePDE 353 8.6 References 354 Table of Contents......Page 0 Engineering Analysis......Page 1 Files Available from CRC Press......Page 3 Dedication......Page 6 Preface and Acknowledgments......Page 7 Contents......Page 9 1.1 Introduction......Page 11 1.2 Manipulation of Matrices......Page 12 1.2 Multiplication of Matrices......Page 14 FORTRAN Version......Page 16 Interactive Operation......Page 18 More Programming Review......Page 20 Sample Applications......Page 26 QuickBASIC Version......Page 28 Sample Applications......Page 30 MATLAB Applications......Page 32 Mathematica Applications......Page 34 1.3 Solution of Matrix Equation......Page 35 QuickBASIC Version of the program CramerR......Page 38 Gaussian Elimination Method......Page 40 Sample Application......Page 44 FORTRAN Version......Page 45 Gauss-Jordan Method......Page 46 QuickBASIC Version......Page 47 FORTRAN Version......Page 48 MATLAB Applications......Page 49 Mathematica Applications......Page 50 1.5 Matrix Inversion, Determinant, and Program MatxInvD......Page 51 QuickBASIC Version......Page 52 FORTRAN Version......Page 53 MATLAB Application......Page 55 Mathematica Applications......Page 56 Transformation of Coordinate Systems, Rotation, and Animation......Page 57 Function Animate1(Ncycle,Damping)......Page 61 QuickBASIC Version......Page 62 Matrix Algebra......Page 64 Gauss......Page 66 Matrix Inversion......Page 67 1.7 Reference......Page 73 2.2 Exact Curve Fit......Page 74 FORTRAN Version......Page 75 Sample Applications......Page 76 MATLAB Application......Page 77 2.3 Program LeastSq1—Least-Squares Linear Curve-Fit......Page 80 QuickBASIC Version......Page 82 FORTRAN Version......Page 83 Transformed Least-Squares Curve-Fit......Page 84 2.4 Program LeastSqG — Generalized Least-Squares CurveFit......Page 87 QuickBASIC Version......Page 89 Sample Applications......Page 90 FORTRAN Version......Page 91 MATLAB Application......Page 92 Mathematica Applications......Page 96 2.5 Program CubeSpln — Curve Fitting with Cubic Spline......Page 97 QuickBASIC Version......Page 100 MATLAB Application......Page 102 Mathematica Applications......Page 105 LeastSq1......Page 109 LEASTSQG......Page 110 Cubic Spline......Page 112 2.7 References......Page 114 3.1 Introduction......Page 115 Incremental Search......Page 116 Bisection Search......Page 117 Newton-Raphson Iterative Method......Page 118 Sample Application......Page 119 FORTRAN Version......Page 120 Sample Application......Page 121 MATLAB Application......Page 122 Method of Successive Substitution......Page 124 Mathematica Applications......Page 125 3.3 Program NewRaphG— Generalized Newton-Raphson Iterative Method......Page 126 Transcendental Equations......Page 127 Extended Newton-Raphson Method......Page 130 FORTRAN Version......Page 131 MATLAB Applications......Page 132 Mathematica Applications......Page 134 3.4 Program Bairstow — Bairstow’s Method for Finding Polynomial Roots......Page 135 QuickBASIC Version......Page 138 FORTRAN Version......Page 139 MATLAB Application......Page 141 Mathematica Applications......Page 142 FindRoot......Page 144 NewRaphG......Page 146 Bairstow......Page 148 3.6 References......Page 149 4.1 Introduction......Page 150 4.2 Program DiffTabl — Applications of Finite-Difference Table......Page 151 Backward-Difference Operator......Page 153 Central-Difference Operator......Page 154 Differentiation Operator......Page 155 QuickBASIC Version......Page 157 FORTRAN Version......Page 158 MATLAB Application......Page 161 Mathematica Applications......Page 164 4.3 Program LagrangI — Applications of Lagrangian Interpolation Formula......Page 168 QuickBASIC Version......Page 170 FORTRAN Version......Page 171 MATLAB Application......Page 172 Mathematica Applications......Page 174 DiffTabl......Page 175 LagrangI......Page 176 4.5 Reference......Page 177 5.1 Introduction......Page 178 5.2 Program NuIntGra — Numerical Integration by Application of the Trapezoidal and Simpson Rules......Page 181 Trapezoidal Rule......Page 185 Simpson’s Rule......Page 186 QuickBASIC Version......Page 190 FORTRAN Version......Page 191 MATLAB Application......Page 192 5.3 Program Volume — Numerical Approximation of Double Integration......Page 193 FORTRAN Version......Page 197 QuickBASIC Version......Page 199 MATLAB Application......Page 200 Mathematica Applications......Page 202 NuIntGra......Page 204 Volume......Page 205 5.5 References......Page 207 6.1 Introduction......Page 208 6.2 Program RungeKut — Application of the Runge-Kutta Method for Solving the Initial-Value Problems......Page 209 Runge-Kutta Method (Fourth-Order)......Page 211 FORTRAN Version......Page 214 Program RungeKut......Page 215 FORTRAN Version......Page 216 QuickBASIC Version......Page 217 FORTRAN Version......Page 218 Sample Applications of the program RungeKut......Page 219 A Nonlinear Oscillation Problem Solved by RungeKut......Page 221 MATLAB Application......Page 224 Mathematica Applications......Page 228 6.3 Program OdeBvpRK — Application of Runge-Kutta Method for Solving Boundary-Value Problems......Page 230 Numerical Examples......Page 232 FORTRAN Version......Page 234 MATLAB Applications......Page 236 Mathematica Applications......Page 238 6.4 Program OdeBvpFD — Application of Finite Difference Method for Solving Boundary-Value Problems......Page 241 Sample Application......Page 247 QuickBASIC Version......Page 248 Sample Applications......Page 249 Membrane Problem......Page 250 Beam Deflection Problem......Page 252 Mathematica Applications......Page 253 RungeKut......Page 254 OdeBvpRK......Page 259 OdeBvpFD......Page 261 6.6 References......Page 263 7.1 Introduction......Page 264 7.2 Programs EigenODE.Stb and EigenODE.Vib — for Solving Stability and Vibration Problems......Page 267 FORTRAN Version......Page 268 Sample Applications......Page 269 Program EigenODE.Vib......Page 270 Sample Application......Page 271 MATLAB Applications......Page 272 7.3 Program CharacEq — Derivation of Characteristic Equationof a Specified Square Matrix......Page 274 QuickBASIC Version......Page 276 FORTRAN Version......Page 277 Sample Application......Page 278 MATLAB Application......Page 279 Mathematica Applications......Page 280 7.4 Program EigenVec — Solving Eigenvector by Gaussian Elimination Method......Page 282 QuickBASIC Version......Page 283 FORTRAN Version......Page 284 Sample Application......Page 285 Mathematica Applications......Page 286 Principal Stresses and Planes......Page 287 Quadratic Forms and Canonical Transformation......Page 290 7.5 Program EigenvIt — Iterative Solution of the Eigenvalue and Eigenvector......Page 292 QuickBASIC Version......Page 293 FORTRAN Version......Page 294 MATLAB Application......Page 295 Mathematica Applications......Page 299 CharacEq......Page 301 EigenVec......Page 303 EigenvIt......Page 304 7.7 References......Page 307 8.1 Introduction......Page 308 8.2 Program ParabPDE — Numerical Solution of Parabolic Partial Differential Equations......Page 309 FORTRAN Version......Page 311 Sample Output......Page 312 MATLAB Applications......Page 313 Mathematica Applications......Page 315 8.3 Program Relaxatn — Solving Elliptical Partial Differential Equations by Relaxation Method......Page 318 FORTRAN Version......Page 322 Sample Results......Page 323 QuickBASIC Version......Page 325 Irregular Boundaries......Page 326 MATLAB Application......Page 327 Mathematica Applications......Page 333 Warping Analysis of a Twisted Bar with Noncircular Cross Section......Page 334 8.4 Program WavePDE — Numerical Solution of Wave Problems Governed by Hyperbolic Partial Differential Equations......Page 339 QuickBASIC Version......Page 341 Sample Application......Page 342 MATLAB Applications......Page 344 Mathematica Application......Page 346 Relaxatn......Page 349 WavePDE......Page 353 8.6 References......Page 354

This book provides a concise introduction to numerical concepts in engineering analysis, using FORTRAN, QuickBASIC, MATLAB, and Mathematica to illustrate the examples. Discussions include:

matrix algebra and analysis

solution of matrix equations

methods of curve fit

methods for finding the roots of polynomials and transcendental equations

finite differences and methods for interpolation and numerical differentiation

numerical computation of single and double integrals

numerical solution of ordinary differential equations Engineering Analysis:

teaches readers to become proficient in FORTRAN or QuickBASIC programming to solve engineering problems

provides an introduction to MATLAB and Mathematica, enabling readers to write supplementary m-files for MATLAB and toolkits for Mathematica using C-like commands The 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.

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Introduces numerical concepts in engineering analysis, using FORTRAN, QuickBASIC, MATLAB, and Mathematica to illustrate examples. Minimum mathematical derivations are given for each numerical method covered, with thorough explanations of computational procedures to solve a specific problem. Emphasis is on interactive operation in developing computer programs. Coverage include matrix algebra and analysis, matrix equations, transcendental equations, and numerical computation of single and double integrals and ordinary differential equations. Annotation c. by Book News, Inc., Portland, Or.

[Mathématiques et statistiques ; informatique ; génie (général) ; génie agroalimentaire]