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.
Author(s): Yen-Ching Pao
Edition: 1
Publisher: CRC Press
Year: 1998
Language: English
Pages: 354
Tags: Математика;Вычислительная математика;
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
