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Bluman G.W. — Similarity Methods for Differential Equations
Bluman G.W. — Similarity Methods for Differential Equations



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Название: Similarity Methods for Differential Equations

Автор: Bluman G.W.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 332

Добавлена в каталог: 29.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\pi$-variable      183
Abramowitz, M.      269
Affine transformation      2 72 112
Airy functions      217 246
Area preserving transformation      53
Asymptotic field      287 289 294
Atkinson, J.      260
Autonomous systems      132
Barenblatt, G.      182
Bauer, L.      137
Bessel functions      217
Bethe, H.      123
Bilinear group      303
Birkhoff, G.      182 198
Blasius equation      130 131 137 199
Bluman, G.      146 207 209 223 238 258 295
Bohr radius      125
boundary conditions      143 145 147 148 152 160 162 172 222 227 230 231
Boundary curve      145 152 160 162 214 222 227 230 231 238 239
Boundary layer on a wedge      198
Breiter, M.      294
Bridgman, P.      182
Brownian motion      258 271
Buckingham Pi-Theorem      183
Burgers, J.      246
Calculus of variations      116
Callegari, A.      137
Canonical coordinates      1 21 22 38 42 43 64 79 96 115 143 161
Canonical coordinates, transformation to      164—166
Cauchy — Riemann equations      53
Caughey, T.      260
Chain rule      158
Classical group      208
Cole, J.      207 209
Commutation      211
Commutator      61 212 303
Commutator table      212 250
Commutator, invariance condition using      62 91
Complex parameters, use of      219 234
Compressible flow      54 287
Confluent hypergeometric equation      215
Conformal transformation      52 113 303
Constant, definition of      188 189
Contact transformation      147
Critical solutions      120
Determining equations      145 156 282 296
Dienes, J.      260
Differential invariant      109
Diffusion equation, nonlinear      130 295
Diffusion equation, Smoluchowski's      275
Dimension matrix      183
Dimension of      183
Dimension vector      184
Dimensional analysis      3 146 166 167 174 181—199
Dimensionless quantity      183
Dimensionless variables      167—169
Dirac delta function      222
Earthworm's Christmas problem      233
Euler — Lagrange equation      117
Exceptional path      128 130 135 176 294
Exceptional solution      126
Extended group      88 103 154
Extended infinitesimal transformation      88 103 104 148 152—155 158
Extended infinitesimal transformation, symbol of      88 104
Extended transformation      84 103 152
Extended transformation, calculation for several variables      157—160
Extended transformation, invariant of      161
Extended transformation, once extended      86 152 154 159
Extended transformation, twice extended      103 152 154 155 159
Falkner — Skan equation      199
Far field      287—294
Fermi — Dirac statistics      124
First extension      152 159
Fluid flow      54 130 192—196 231—233 287
Fokker — Planck equation      258—274
Functional form of similarity solution      144 172
Fundamental dimensional unit      182
Fundamental solutions of Euler — Poisson — Darboux equation      256
Fundamental solutions of heat equation      167 179 221—230
Fundamental solutions of telegraph equation      255
Fundamental solutions of wave equation      251—255 256
Galilean transformation      210
Gas dynamics      147
General similarity solution      213
Global transformation      6 17 26 118 170
Global transformation, construction from infinitesimal      26
Global transformation, series representation of      45 81
Greub, W.      166
Group      13 15 23 157
Group, admitted by differential equation      54 59 71 89 92 94 101 107 148
Group, composition      15 16 21 23 27 31 37
Group, extended      88 103 154
Group, finding      92 148 152
Group, heat equation      206—210 303—315
Group, infinitesimals of      144
Group, multi-parameter      16 146 166 221—226 258 261 278 303
Group, one-parameter      15 23 31 77 147 149 157
Guderley, K.      286 291 293 294
Heat equation      146 147 166 206 295 303
Heat equation, fundamental solutions of      167 221—230
Heat equation, group properties of      146 147 206—210 303—315
Heat equation, nonlinear      295—302
Hermite functions      174
Hermite polynomials      216
Hodograph transformation      162
Homogeneous equation      66
Incompressible flow      54 130
Infinite-parameter group      146 282—286
Infinitesimal generator      51 88
Infinitesimal operator      203 210 260
Infinitesimal rotation      19 39 45
Infinitesimal screw      80
Infinitesimal transformation      16 25 26 31 36 144 147 150 157
Infinitesimal transformation, extended      87 148 154 158 305
Infinitesimal transformation, finding      152 155 156
Infinitesimal transformation, leaving invariant p.d.e.      145 148 152
Infinitesimal transformation, symbol of      36 39 88
Infinitesimal transformation, three variables      78
Infinitesimal transformation, uniqueness of      31
Integrating factor      61 67
Integrating factor, geometric interpretation of      67
Invariance      7 46 147 149 155 160 161 201 307
Invariance, condition      46 48 56 57 62 94 101 105 138 155 160 161 172
Invariance, criterion for a surface      84 89
Invariant boundary condition      161 222 227 230 231
Invariant boundary curve      145 161 214 222 227 230 231 238 239
Invariant coordinates      112 133 176
Invariant curve      18 20 22 47—49 83 109
Invariant differential      109
Invariant differential equation      109 111 138 161
Invariant family of curves      54 56
Invariant function      18 20 22 46 49 81
Invariant path curve      18 20 46
Invariant point      22 47 49 83
Invariant surface      83 94 151
Invariant surface condition      144 150 172 185 205 225 260 318
Invariants, finding      108 111 114 115 116
Invariants, functionally independent      173 188 262
Invariants, mutually distinct      262
Inverse Stefan problem      235—245
Jacobi's identity      211
Jacobian      165 320
Kronecker delta symbol      158
Kummer's hypergeometric function      269
Lagerstrom, P.      197
Landau, H.      239
Langford, D.      236 239
Laplace's equation      282 291 302 303
Laurent series expansion      283
Lie algebra      211 304
Lie group      143
Lie, S.      61 146 147 207
Limiting Mach wave      291 293
Linear ordinary differential equation      112
Linear ordinary differential equation, group for      73 112
Linear second order p.d.e.      205
Linear second order p.d.e., determining equations for      156
Lorentz transformation      255
Mach lines      287
Mach number      287
Mach waves      288 291
Matschat, K.      146 147 293
Miele, A.      116
Milinazzo, F.      238
Modified Bessel functions      272
Moebius group      303
Moments      259 272 274 276 282
Momentum equation      131
Mueller, E.A.      146 147 293
Multi-parameter group      16 146 166 221—226 258 261 278 303
Navier — Stokes equations      130
Near field      291
Neuringer, J.      275
Node      293
Nonlinear diffusion equation      130 147 295—301
Nonlinear wave equation      301 302
Nonsingular solution      119
Null space      191
One-parameter group      15 23 31 77 147 149 156
Operators, extended      107
Operators, infinitesimal      203
Operators, total derivative      158
Orthogonal trajectories      64
Ovsjannikov, L.V.      146 147 248 295
Parabolic cylinder functions      215
Parameterization      25 31
Path curves      17 20 22 44 51 82 94 118 151
Path curves, interpretation of      54
Path curves, invariant      18 20 46
Path curves, one-parameter family of      17
Perspective transformation      30 73 111
Perturbation field      287
Phase plane      133 137 257
Planck's constant      124
Point transformation      101
Poisson equation      124
Poisson kernel      146 282—286
Polynomial p.d.e.      156
probability distribution      258
Probability distribution, stable      259
Projective transformation      50 53 59 84 105 210
Quantity, definition of      182
Quasilinear p.d.e's, system of first order      147
Randall, D.      293
Range space      191
Ratio of specific heats      256 287
Rayleigh flow      193—197 231—233
Reflecting boundary      259 269
Reflection, solution by      180 227
Regular solution      291
Reiss, E.      137
Repeated index      157
Riccati equation      94 108 113 176 178
Riemann function      256
Rotation group      18 35 39 41 46 57 58 64 73 88 97
Saddle point      128 293
Sanders, R.      236 239
Schlichting, H.      192
Screw transformation      78
Second extensions      152 159
Sedov, L.      182
Self-similar solutions      182
Separation of variables      218 239 242 247
Shallow membrane equations      137
Similarity      3
Similarity solutions      130 136 143 144 180 213 270
Similarity solutions, superposition of      229 230
Similarity transformation      30
Similarity transformation, variable      11 145 151 197 213 261
Similarity, curve      151
Similarity, form      130 147 151 175 181 219 261
Singular points      119 126 135 293
Singular solution      128
Smoluchowski's diffusion equation      275
Sonic line      287 288 291 293
Special path      120
Stable probability distribution      259
Stationary Markov process      258 276
Stegun, I.      269
Stochastic differential equation      258
Stream function      54 130 199
streamline      54 132
Stretching group      21 34 42 64 73 97 111 146 166 170 185 289
Stretching group, connection with dimensional analysis      170 181—199
Stretching group, examples of invariance under      117 125 132 134 200
Subalgebra      145 303 304
Subcritical solutions      120
Subgroup      145 152 296 303
Subsonic region      288
Supercritical solutions      121
Supersonic region      288
Systems of p.d.e.'s      157
Systems of p.d.e.'s, reduction of number of variables for      160 166
Szaniawski, A.      293
Telegraph equation      255
Thomas — Fermi equation      123
Three variables, infinitesimal transformation for      78
Three variables, one-parameter group in      74
Total derivative operator      158
Transformations, affine      21 72 112
Transformations, area preserving      53
Transformations, conformal      52 113 303
Transformations, contact      147
Transformations, extended      84 86 103
Transformations, global      17 26 118 170
Transformations, hodograph      172
Transformations, infinitesimal      16 25 26 31 36
Transformations, perspective      30 73 111
Transformations, point      101
Transformations, projective      50 53 59 84 105 210
Transformations, screw      78
Transformations, similarity      30
Transitional probability density distribution      258
Translation invariance      162 167 289
Translation invariance, connection with first order o.d.e.'s      4 71 97
Translation invariance, examples of      132 200
Transonic flow      286—295
Variable, definition of      188 189
Watson, G.      272
Wave equation      144 248—257
Weyl, H.      130
Zel'dovich, Y.      182
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