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أخواني في الله أحضرت لكم كتاب Matlab for Engineering Berardino D'Acunto University of Naples Federico II, Italy
![كتاب Matlab for Engineering M_f_e_13](https://i.servimg.com/u/f61/15/36/74/14/m_f_e_13.jpg) و المحتوى كما يلي :
Contents Preface v Chapter 1. Function Files 1 1.1 Matrices 1 1.1.1 Creating Matrices 1 1.1.2 Matrix Indexing . 2 1.1.3 Matrix Manipulation 4 1.1.4 Tridiagonal Matrices . 6 1.1.5 Matrix Operations 8 1.1.6 Right and Left Divisions 9 1.2 Script Files 10 1.2.1 For Loop . 10 1.2.2 Examples of Script Files 11 1.3 Introduction to Function Files 15 1.3.1 Structure of Function Files . 15 1.3.2 Function with a Multiple Output Variable 17 1.3.3 Flow Control Structures . 19 1.3.4 Local Functions, Anonymous Functions 25 1.3.5 Logical Operators and Logical Functions . 27 1.4 Exercises 33 Chapter 2. The Finite Difference Method 39 2.1 Finite Difference Approximations of Derivatives 39 2.1.1 Forward, Backward and Central Approximations . 39 viiviii Matlab for Engineering 2.1.2 Approximation of Functions Depending on Two Variables . 46 2.1.3 Approximation of Higher Order Derivatives 47 2.2 Diffusion 49 2.2.1 Fourier’s Law and Heat Equation . 49 2.2.2 Fick’s Law and Diffusion 55 2.2.3 Free Boundary Value Problems . 56 2.3 Finite Difference Method . 58 2.3.1 Explicit Euler Method 58 2.3.2 Stability, Convergence, Consistence 64 2.3.3 Boundary Value Problems . 68 2.3.4 Diffusion in a Multi-layer Medium . 76 2.3.5 Implicit Euler Method 80 2.3.6 Crank–Nicolson Method . 84 2.3.7 Von Neumann Stability Criterium . 89 2.4 Exercises 93 Chapter 3. Diffusion and Convection 99 3.1 Convection-diffusion Equation 99 3.1.1 Upwind Method . 99 3.1.2 Other Finite Difference Methods for the Convection-Diffusion Equation . 107 3.1.3 Advection Equation . 111 3.2 Method of Lines . 118 3.2.1 Heat Equation 118 3.2.2 Nonlinear Equations . 127 3.2.3 Variable Diffusivity Coefficient . 133 3.2.4 Convection-Diffusion Equation . 136 3.3 Saving Data and Figures . 140 3.3.1 Save Function 140 3.3.2 Load Function 142 3.3.3 Saving Figures 143 3.4 Exercises 143 Chapter 4. Introduction to the Finite Element Method 153 4.1 Numerical Integration 153 4.2 Finite Element Method . 164 4.2.1 Axial Motion of a Bar 164 4.2.2 Weak Solution 167Contents ix 4.2.3 Shape Functions . 169 4.2.4 Boundary Value Problems . 171 4.2.5 Axial Displacement and Stress in a Bar 180 4.2.6 Concentrated Force and Dirac Function 184 4.3 Partial Differential Equations 189 4.3.1 Diffusion Equation 189 4.3.2 Wave Equation 197 4.4 Exercises 205 Chapter 5. Introduction to the Finite Element Method in Two Spatial Dimensions 213 5.1 Elliptic Partial Differential Equations 213 5.1.1 Green’s Identities 213 5.1.2 Boundary Value Problems . 214 5.2 Finite Element Method in Two Spatial Dimensions 217 5.2.1 Shape Functions . 217 5.2.2 Weak Form of the Poisson Equation 225 5.2.3 Dirichlet–Neumann Problem 230 5.2.4 Applications to the Dam and Sheet Pile Wall . 234 5.3 Finite Difference Method . 240 5.3.1 Five-Point Method 240 5.3.2 Model of a Dam . 247 5.4 Exercises 257 Chapter 6. The Euler–Bernoulli Beam 267 6.1 Finite Element Method . 267 6.1.1 Euler–Bernoulli Beam Equation 267 6.1.2 Shape Functions . 270 6.1.3 Weak Form 274 6.2 Statics . 277 6.3 Beam Subjected to Concentrated Forces 296 6.4 Exercises 305 Bibliography 311 Index 313 Index < (less), Matalab operator, 20 <= (less or equal), Matalab operator, 20 >= (greater or equal), Matalab operator, 20 >= (greater), Matalab operator, 20 == (equal), Matalab operator, 20 ˜= (not equal), Matalab operator, 20 abs, Matlab command, 42 all, logical function, Matlab, 30 anonymous function, Matlab, 26 any, logical function, Matlab, 31 axis, Matlab command, 13 backward, function file, 93 beam c pn pn, function file, 297 beam fx fr, function file, 282 beam fx fx uA, function file, 293 beam fx pn, function file, 288 beam ov, function file, 303 beam pn pn, function file, 285 Bessel, historical note, 158 besselj, Matlab command, 158 break, Matlab command, 24 burgers, function file, 128 Burgers, historical note, 127 central, function file, 43 central implicit, function file, 108 clc, Matlab command, 12 consolidation1, function file, 121 consolidation2, function file, 125 crank, function file, 86 Crank, historical note, 85 dam, function file, 235 dam 5p, function file, 254 Darcy, historical note, 49 diag, Matlab command, 5 diffusion d, function file, 192 diffusion n, function file, 195 Dirac δ function, 184 Dirac, historical note, 184 Dirichlet boundary condition, 52 Dirichlet, historical note, 52 disp, Matlab command, 13 error, Matlab command, 20 errordlg, Matlab command, 20 Euler, historical note, 39 Euler–Bernoulli equation, 268 Euler–Lagrange equation, 268 euler e, function file, 60 euler edn, function file, 72 euler el, function file, 92 euler em, function file, 62 euler en, function file, 70 euler enm, function file, 71 euler i, function file, 81 eye, Matlab command, 4 fem dd, function file, 174 fem dn, function file, 177 313314 Matlab for Engineering feval, Matlab command, 26 Fick’s law, 55 Fick, historical note, 49 find, logical function, Matlab, 31 five point, function file, 243 five point f1, function file, 246 for, Matlab structure, 10 forward, function file, 41 Fourier’s law, 49 Fourier, historical note, 49 fplot, Matlab command, 27 fprintf, Matlab command, 42 ftbs, function file, 113 ftfs, function file, 115 full, Matlab command, 7 function file, Matlab, 15 Gauss, historical note, 51 gradient, Matlab command, 17 Green’s identities, 214 Green, historical note, 214 hermitian functions, 271 hold off, Matlab command, 122 hold on, Matlab command, 121 homogeneous boundary condition, 53 Hooke, historical note, 165 if-elseif-else, Matlab structure, 19 int, Matlab command, 155, 160 integral, Matlab command, 155 integral2, Matlab command, 160 integral 1, function file, 155 integral 2, function file, 156 integral 2D 1, function file, 160 integral 2D 2, function file, 205 integral 2D 3, function file, 163 integral 2D 4, function file, 163 integral 3, function file, 157 integral 4, function file, 158 ismember, logical function, Matlab, 32 isspace, Matlab command, 25 Kronecker δ function, 169 Kronecker, historical note, 169 Lagrange, historical note, 169 laplace, function file, 229 Laplace, historical note, 52 layers, function file, 77 left division, Matlab, 10 legend, Matlab command, 13, 21 lines c d 1, function file, 137 lines c d 2, function file, 138 lines heat1, function file, 123 linspace, Matlab command, 3 load, Matlab command, 142 local function, Matlab, 25 logical operators, Matlab, 27 mass, function file, 276 max, Matlab command, 42 Neumann boundary condition, 52 Neumann, historical note, 52 Newton, historical note, 53 Nicolson, historical note, 85 nonlinear, function file, 131 norm, Matlab command, 96 num2str, Matlab command, 13 ode15s, Matlab command, 132 ode45, Matlab command, 121 ones, Matlab command, 4 P´eclet, historical note, 100 pause(s), Matlab command, 13 pause, Matlab command, 15 plot, Matlab command, 13 Poisson, historical note, 214 pure Neumann problem, 179 pyramid, function file, 223 pyramid phi, function file, 225 quiver, Matlab command, 18 Rectangle Rule, 153 rectangle, Matlab command, 18 relational operators, Matlab, 20 repmat, Matlab command, 7 reshape, Matlab command, 5 right division, Matlab, 9Index 315 Robin boundary condition, 53 Robin, historical note, 53 save, Matlab command, 141 sheet pile wall, function file, 262 Simpson Rule, 154 Simpson, historical note, 154 simpson, function file, 156 simpson2d, function file, 161 size, Matlab command, 29 spdiags, Matlab command, 6 spy, Matlab command, 7 sqr, function file, 15 Stefan condition, 57 Stefan problem, 58 Stefan, historical note, 57 stiffness, function file, 276 stiffness s, function file, 306 strcat, Matlab command, 23 stress 1, function file, 181 stress 2, function file, 210 surf, Matlab command, 15 switch, Matlab structure, 22 sym, Matlab command, 156 symbol O, 40 Taylor, nota storica, 40 test function, 167 tic, Matlab command, 123 title, Matlab command, 13 toc, Matlab command, 124 transpose matrix, Matlab, 1 Trapezium Rule, 154 triangulation plot1, function file, 217 triangulation plot2, function file, 218 type, Matlab command, 142 upper, Matlab command, 23 upwind, function file, 101 variable1, function file, 134 Von Neumann criterium, 89 Von Neumann, historical note, 89 wave d, function file, 200 wave n, function file, 203 while, Matlab structure, 24 whos, Matlab command, 7 xlabel, Matlab command, 13 ylabel, Matlab command, 13 Young, historical note, 165 zeros, Matlab command, 4 zlabel, Matlab command, 15 #ماتلاب,#متلاب,#Matlab,
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