MATLAB Mathematics - SERC - Index of

More documents

Recommendations

Info

2 Polynomials and Interpolation Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Polynomial Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Representing Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 Polynomial Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 Characteristic Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4 Polynomial Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4 Convolution and Deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Polynomial Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Polynomial Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6 Partial Fraction Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9 Interpolation Function Summary . . . . . . . . . . . . . . . . . . . . . . . . 2-9 One-Dimensional Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . 2-10 Two-Dimensional Interpolation . . . . . . . . . . . . . . . . . . . . . . . . 2-12 Comparing Interpolation Methods . . . . . . . . . . . . . . . . . . . . . . 2-13 Interpolation and Multidimensional Arrays . . . . . . . . . . . . . . 2-15 Triangulation and Interpolation of Scattered Data . . . . . . . . . 2-18 Tessellation and Interpolation of Scattered Data in Higher Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26 Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-37 3 Fast Fourier Transform (FFT) Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 Finding an FFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2 Example: Using FFT to Calculate Sunspot Periodicity . . . . . . . 3-3 Magnitude and Phase of Transformed Data . . . . . . . . . . . . . 3-7 FFT Length Versus Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9 ii Contents
Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10 4 Function Functions Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2 Representing Functions in MATLAB . . . . . . . . . . . . . . . . . . . . 4-3 Plotting Mathematical Functions . . . . . . . . . . . . . . . . . . . . . . . 4-5 Minimizing Functions and Finding Zeros . . . . . . . . . . . . . . . 4-8 Minimizing Functions of One Variable . . . . . . . . . . . . . . . . . . . . 4-8 Minimizing Functions of Several Variables . . . . . . . . . . . . . . . . 4-9 Fitting a Curve to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10 Setting Minimization Options . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13 Output Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14 Finding Zeros of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21 Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25 Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26 Numerical Integration (Quadrature) . . . . . . . . . . . . . . . . . . . 4-27 Example: Computing the Length of a Curve . . . . . . . . . . . . . . 4-27 Example: Double Integration . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28 Parameterizing Functions Called by Function Functions 4-30 Providing Parameter Values Using Nested Functions . . . . . . 4-30 Providing Parameter Values to Anonymous Functions . . . . . . 4-31 5 Differential Equations Initial Value Problems for ODEs and DAEs . . . . . . . . . . . . . . 5-2 ODE Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 iii
Page 1 and 2: MATLAB® The Language of Technical
Page 3: Revision History June 2004 First pr
Page 8 and 9: Introduction to Initial Value ODE P
Page 10 and 11: vi Contents
Page 12 and 13: 1 Matrices and Linear Algebra Funct
Page 14 and 15: 1 Matrices and Linear Algebra Matri
Page 16 and 17: 1 Matrices and Linear Algebra Addin
Page 18 and 19: 1 Matrices and Linear Algebra If x
Page 20 and 21: 1 Matrices and Linear Algebra y = v
Page 22 and 23: 1 Matrices and Linear Algebra Vecto
Page 24 and 25: 1 Matrices and Linear Algebra backs
Page 26 and 27: 1 Matrices and Linear Algebra If A
Page 28 and 29: 1 Matrices and Linear Algebra You c
Page 30 and 31: 1 Matrices and Linear Algebra 0.9 0
Page 32 and 33: 1 Matrices and Linear Algebra Inver
Page 34 and 35: 1 Matrices and Linear Algebra X = p
Page 36 and 37: 1 Matrices and Linear Algebra There
Page 38 and 39: 1 Matrices and Linear Algebra The e
Page 40 and 41: 1 Matrices and Linear Algebra The L
Page 42 and 43: 1 Matrices and Linear Algebra In co
Page 44 and 45: 1 Matrices and Linear Algebra Matri
Page 46 and 47: 1 Matrices and Linear Algebra compu
Page 48 and 49: 1 Matrices and Linear Algebra Eigen
Page 50 and 51: 1 Matrices and Linear Algebra produ
Page 52 and 53: 1 Matrices and Linear Algebra Singu
Page 54 and 55: 1 Matrices and Linear Algebra 1-44
Page 56 and 57:
2 Polynomials and Interpolation Pol
Page 58 and 59:
2 Polynomials and Interpolation pol
Page 60 and 61:
2 Polynomials and Interpolation Cal
Page 62 and 63:
2 Polynomials and Interpolation whe
Page 64 and 65:
2 Polynomials and Interpolation Int
Page 66 and 67:
2 Polynomials and Interpolation int
Page 68 and 69:
2 Polynomials and Interpolation 2 G
Page 70 and 71:
Page 72 and 73:
2 Polynomials and Interpolation for
Page 74 and 75:
2 Polynomials and Interpolation Con
Page 76 and 77:
2 Polynomials and Interpolation Lat
Page 78 and 79:
2 Polynomials and Interpolation −
Page 80 and 81:
2 Polynomials and Interpolation −
Page 82 and 83:
2 Polynomials and Interpolation 7 3
Page 84 and 85:
2 Polynomials and Interpolation T =
Page 86 and 87:
2 Polynomials and Interpolation Bec
Page 88 and 89:
Page 90 and 91:
2 Polynomials and Interpolation 2-3
Page 92 and 93:
2 Polynomials and Interpolation 2-3
Page 94 and 95:
3 Fast Fourier Transform (FFT) Intr
Page 96 and 97:
3 Fast Fourier Transform (FFT) 200
Page 98 and 99:
3 Fast Fourier Transform (FFT) 2 x
Page 100 and 101:
3 Fast Fourier Transform (FFT) 500
Page 102 and 103:
3 Fast Fourier Transform (FFT) Func
Page 104 and 105:
4 Function Functions Function Summa
Page 106 and 107:
4 Function Functions You can also c
Page 108 and 109:
4 Function Functions 25 20 15 10 5
Page 110 and 111:
4 Function Functions Minimizing Fun
Page 112 and 113:
4 Function Functions To try fminsea
Page 114 and 115:
4 Function Functions Plotting the R
Page 116 and 117:
4 Function Functions The number of
Page 118 and 119:
4 Function Functions and displays t
Page 120 and 121:
4 Function Functions end function s
Page 122 and 123:
4 Function Functions States of the
Page 124 and 125:
4 Function Functions 100 80 60 40 2
Page 126 and 127:
4 Function Functions You can verify
Page 128 and 129:
4 Function Functions Troubleshootin
Page 130 and 131:
4 Function Functions A three-dimens
Page 132 and 133:
4 Function Functions Parameterizing
Page 134 and 135:
4 Function Functions “Anonymous F
Page 136 and 137:
5 Differential Equations Initial Va
Page 138 and 139:
5 Differential Equations odephas3 o
Page 140 and 141:
5 Differential Equations This secti
Page 142 and 143:
5 Differential Equations The basic
Page 144 and 145:
5 Differential Equations 2 Code the
Page 146 and 147:
5 Differential Equations function.
Page 148 and 149:
5 Differential Equations One way to
Page 150 and 151:
5 Differential Equations y0, yp0 Ve
Page 152 and 153:
5 Differential Equations For exampl
Page 154 and 155:
5 Differential Equations 1 0.8 0.6
Page 156 and 157:
5 Differential Equations 2.5 Soluti
Page 158 and 159:
5 Differential Equations To run thi
Page 160 and 161:
5 Differential Equations 2 u′ i =
Page 162 and 163:
5 Differential Equations dydt(i+1,:
Page 164 and 165:
5 Differential Equations refine = 4
Page 166 and 167:
5 Differential Equations Example: A
Page 168 and 169:
5 Differential Equations function [
Page 170 and 171:
5 Differential Equations Note The R
Page 172 and 173:
5 Differential Equations 1 Robertso
Page 174 and 175:
5 Differential Equations The MATLAB
Page 176 and 177:
5 Differential Equations Summary of
Page 178 and 179:
5 Differential Equations Problem Si
Page 180 and 181:
5 Differential Equations Error Tole
Page 182 and 183:
5 Differential Equations Troublesho
Page 184 and 185:
5 Differential Equations Function d
Page 186 and 187:
5 Differential Equations dde23 prod
Page 188 and 189:
5 Differential Equations The exampl
Page 190 and 191:
5 Differential Equations solution y
Page 192 and 193:
5 Differential Equations Example: C
Page 194 and 195:
5 Differential Equations Changing D
Page 196 and 197:
5 Differential Equations BVP Functi
Page 198 and 199:
5 Differential Equations two-point
Page 200 and 201:
5 Differential Equations The input
Page 202 and 203:
5 Differential Equations 2 Pass the
Page 204 and 205:
Page 206 and 207:
5 Differential Equations Finding Un
Page 208 and 209:
5 Differential Equations vectorized
Page 210 and 211:
5 Differential Equations There is a
Page 212 and 213:
5 Differential Equations 3 Solve on
Page 214 and 215:
5 Differential Equations hold off T
Page 216 and 217:
5 Differential Equations Note The d
Page 218 and 219:
5 Differential Equations legend('An
Page 220 and 221:
5 Differential Equations Here, v(1-
Page 222 and 223:
5 Differential Equations solution v
Page 224 and 225:
5 Differential Equations Note The D
Page 226 and 227:
5 Differential Equations After disc
Page 228 and 229:
5 Differential Equations The output
Page 230 and 231:
Page 232 and 233:
5 Differential Equations Note See t
Page 234 and 235:
5 Differential Equations The exampl
Page 236 and 237:
5 Differential Equations and the ri
Page 238 and 239:
5 Differential Equations u1(x,t) 1
Page 240 and 241:
5 Differential Equations Selected B
Page 242 and 243:
6 Sparse Matrices Function Summary
Page 244 and 245:
6 Sparse Matrices Function Summary
Page 246 and 247:
6 Sparse Matrices This matrix requi
Page 248 and 249:
6 Sparse Matrices S = (3,1) 1 (2,2)
Page 250 and 251:
6 Sparse Matrices Now F = full(S) d
Page 252 and 253:
6 Sparse Matrices Importing Sparse
Page 254 and 255:
6 Sparse Matrices west0479 west0479
Page 256 and 257:
6 Sparse Matrices The find Function
Page 258 and 259:
6 Sparse Matrices of the rows and c
Page 260 and 261:
6 Sparse Matrices The vertices of o
Page 262 and 263:
6 Sparse Matrices 0 10 20 30 40 50
Page 264 and 265:
6 Sparse Matrices 0 500 1000 1500 2
Page 266 and 267:
6 Sparse Matrices simply sparse(m,n
Page 268 and 269:
6 Sparse Matrices Similarly, S(:,p)
Page 270 and 271:
6 Sparse Matrices The following MAT
Page 272 and 273:
6 Sparse Matrices 0 Original 0 Reve
Page 274 and 275:
6 Sparse Matrices QR Factorization
Page 276 and 277:
6 Sparse Matrices shows that A has
Page 278 and 279:
6 Sparse Matrices Functions for Ite
Page 280 and 281:
6 Sparse Matrices set up the five-p
Page 282 and 283:
6 Sparse Matrices Manipulating Spar
Page 284 and 285:
6 Sparse Matrices Selected Bibliogr
Page 286 and 287:
Index comparing sparse and full mat
Page 288 and 289:
Index H hb1dae demo 5-35 hb1ode dem
Page 290 and 291:
Index nonstiff ODE examples rigid b
Page 292 and 293:
Index LU factorization 6-30 minimum
Page 294:
Index twobvp demo 5-63 two-dimensio
show all

MATLAB Mathematics - SERC - Index of

Create successful ePaper yourself

Delete template?

Save as template?