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Cantwell B.J., Crighton D.G. (Ed), Ablowitz M.J. (Ed) — Introduction to Symmetry Analysis
Cantwell B.J., Crighton D.G. (Ed), Ablowitz M.J. (Ed) — Introduction to Symmetry Analysis

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Название: Introduction to Symmetry Analysis

Авторы: Cantwell B.J., Crighton D.G. (Ed), Ablowitz M.J. (Ed)

Аннотация:

This text offers a broad, self-contained, introduction to the basic concepts of symmetry analysis and is intended primarily for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. The software requires Mathematica 2.2 or higher. MathReader 4.0 is included to permit the user without access to Mathematica to read the sample notebooks and follow the procedure used to find symmetries.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 654

Добавлена в каталог: 27.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      9 10 123 124
Abelian Lie algebra      139
Abramowitz, M.      262 275
Acceleration field      353
Acceleration field gradient      354
action      99 105
Action integral      99 105 499 500
Action of a harmonic oscillator      108
Affine transformation      85
Aksenov, A.V.      275
Allen, G.A.      363
Alternating unit tensor      59
Ames, W.F.      3 31 516 550
Analytic function      128 129 185
Anderson, R.L.      3 31 447 497 513 550 569 570 583
Andreev, V.K.      3 31 364 393
angular momentum      111 506 507
Apogee      114
Area of an elliptic orbit      115
Ashkenas, H.      394
Ashley, H.      394
Associativity      10 130
Associativity of a Lie group      125
Auto-Backlund transformation      516 549
Autonomous      56
Autonomous infinite order system of ODEs      452
Autonomous pair of ODEs in the plane      55 86 168 287 310
Autonomous particle path system      79 130 338 358 404
Autonomous system of ODEs      125
Axi-symmetric Laplace equation      275
Axially symmetric wave equation      274
Backlund transformations      515
Backlund transformations for Burgers equation      530
Backlund transformations for the KdV equation      541
Backlund transformations for the Liouville equation      517
Backlund transformations sine-Gordon equation      519
Baikov, V.A.      269 275
Bailey, A.B.      46 48 54
Barenblatt, G.I.      3 21 31 32 44 51 54 262 275
Barone, A.      534 550
Bashforth, F.A.      46 47 54
Batchelor, G.K.      xix 317 444
Baumann, G.      3 32 272 275 276
Beaupre, G.      54
Bernoulli relation      280 385
Bianchi permutation relation      521 548
Bianchi, L.      521 550
Bifurcation      325 330 335 339 348 352
Binary operation of composition      123
Binomial series      135
Binomial series Blasius      281 439
Binomial series Blasius equation      179 219 278 284 471 596
Binomial series invariant group      219
Binomial series similarity variables      282
Binomial series thermal analogy      299
Birkhoff, G.      3
Birkhoff, G.D.      2 31
Blackburn, H.M.      445
Blaom, A.D.      120
Blasius, H.M.      278 281 317
Blast wave problem      375
Blast wave problem in 2D      392
Bluman, G.      3 31 142 148 219 236 272 276 324 362 447 479 497
Boulton, A.      599
Boundary layers      277
Boundary layers stream function equation      301 305
Boundary layers stream function equation invariant group      301
Boundary layers unsteady      302 316
Boundary layers unsteady invariant group      302
Boundary layers with pressure gradient      301
Boussinesq approximation      315 407
Bradshaw, P.      444
Brahc, Tycho      34
Bridgeman, P.W.      47 54
Browand, F.K.      444
Brown, G.L.      395 444
Bryant, R.L.      599
Buchnev, A.A.      362
Buckingham Pi theorem      12 47 283
Buoyancy induced flow      316
Buoyant jet      440
Burgers equation      180 486
Burgers equation Backlund transformation for      530
Burgers equation Burgers potential equation      22 481
Burgers equation integro-differential operator for      486 522
Burgers equation kinetic energy      548
Burgers equation N wave solution      549
Burgers equation nonlocal group      527 528 548
Burgers equation point group for      482 486
Burgers equation relation to turbulence      530
Burgers equation single hump solution      531
Burgers equation solution      524
Burgers, J.M.      441 445 522 550
Burke — Schumann flame      273
Canonical coordinates      162 163
Canonical coordinates reduction of order by      215
Cantwell, B.J.      54 95 177 362 363 444 445
Cardano formula      89
Cardano formula surface      89
Cardano, Girnlamo      88
Cauchy initial value problem      278 291 294
Cauchy — Riemann conditions      60 92
Central force field      35 111 112 506
Centrifugal energy      513
Chacin, J.M.      445
Chain rule      179 552
Characteristic equations      57 71 81 107 121 130 162 202 206 247 326 338
Characteristic equations Lagrange and Charpit method      74
Characteristic equations Lagrange method      70 82 204
Characteristic function      255 256 451 458
Characteristic surface      80
Characteristics      56 64
Characteristics family of      56
Characteristics in n dimensions      79 81
Chen, J.H.      427 445
Cheng, W.P.      434
Chern, S.S.      599
Chester, W.      3 31
Chong, M.S.      95 445
Chord line      304 385
Chord-tangent construction      173 174
Chorin, A.      444
Circular cylinder drag      42 43
Circular cylinder wake      322
Circulation      441
Clairaut equation      166
Clarkson, P.A.      272 276 551
Closure      9 124 125
Cohen, A.      3 31
Cole — Hopf transformation      529
Cole, J.D.      3 31 272 276 394 530 550
Coles, D.      54 330 362 363 413 415 420 444
Colliding solitons      545
Coloumb gauge      74
Commutator definition      135
Commutator definition table, Blasius equation group      221
Commutator definition table, heat equation group      253
Commutator definition table, projective group      137 138 599
Complete set of orthogonal functions      262
Complete solution      77
Complex lamellar field      73
Complimentary error function      21
Composition of groups      122 123 124 125
Compressible Euler equations      365
Compressible flow      364 549
Confluent hypergeometric functions      261
Conic section      114
Conservation law      119 495 498 504
Conservation of energy      505 507
Conserved integral      258 265 325 334 438
Conserved vector      504
Constant of the motion      98
Contact between a curve and a surface      552
Contact conditions      187 189 192 245 246 448
Contact conditions first order      187 238
Contact conditions higher order      189
Contact conditions infinite order      448
Contact conditions invariance of      200 201 558
Contact transformation      67 453 496
Continuity equation      30 68 280 323 365
Coordinate independence      11
Covariance principle of      10 11 20 33 39 40
Covariant vector      101
Cox, A.B.      54
Critical points classification in 2D      86
Critical points classification in 3D      89 91
Critical points in a turbulent vortex ring      418
Critical points in the unsteady round jet      344 345 346
Critical points linear      84 88
Critical points nonlinear      87
Critically damped      117
Cubic discriminant      89 168 173 340 427
Cubic equation      88
Curl of a vector      58
Curly brace notation      15 183
Cylindrical coordinates, two body problem      111
Damped, linear second order system      116
Damping coefficient      116
Darboux, G.      521 550
Darcy’s law      263
Daykin, D.E.      53 54
de Vries, G.      533 550
Determining equations      178 209 212 237 248 584 587 591
Determining equations method of solution      130
Deviation function      99
Diffeomorphism      13 23 446
Differentiable manifold      58
Differential      80 552
Differential 1-form      58 60
Differential consequences      463
Differential function      129 178 179 186 499
Differential function definition of      185
Differential variables      185 448
Differential volume      59
Differential volume transformation of      499
Diffusion coefficient      19
Diffusion equation with shearing convection      275
Diffusivity      20 254
Diffusivity of pressure      264
Dilation group      18 39 126 133 158 168
Dilation group blast wave problem      379
Dilation group Clairault equation      166
Dilation group heat equation      18
Dilation group Kepler system      116
Dilation group Navicr — Stokcs equations      30 283 313 320 330 336
Dilation group nonlinear heat equation      293
Dilation group stream function equation      281
Dimension, definition of      33
Dimensional analysis      33 283
Dimensional homogeneity      11 12
Dimotakis, P.      363
Diophantene construction      173 357
Diophantus      173
Dirac delta function      336
Discrete groups      10
Discriminant of a cubic equation      89
Discriminant of a quadratic equation      85
dispersion      533
Dissipation of turbulent kinetic energy      400 419
Diverging channel      325
Dorodnitsyn, V.      32
Drag coefficient      41 47
Drag of a circular cylinder      42 43
Drag of a sphere      38 44 46 47 48
dragging      132
Dual stream function      69
Duffy, B.R.      329 362
D’Alembert’s paradox      304
d’Alembert’s principle      96 97
Earth diameter and mass      35
Eccentricity      35 38 114 510
Eigenvalues of a cubic      90
Eigenvectors      86 296
Einstein derivative notation      24
Einstein summation convention      15 80
Einstein, A.      xxxiii xl 24 32
Elliptic curve      172
Elliptic curve 3D flow patterns      353
Elliptic function      170 171
Elliptic integral      170
Elliptical orbit      35 114
Energy dissipation integral      548
Engel, F.      xli
Ensemble mean      397
Enthalpy      66 68 92 370
Entrainment velocity      439
entropy      66 67 378
Equation of state      66
Equation of state ideal gas      67 370
Equivalence classes of transformations      457
Ergodic theorem      2
Error function, complimentary      21
Esposito, F      550
Estabrook, F.B.      3 31
Euler equations, compressible      365
Euler equations, incompressible      401
Euler operator      502
Euler — Lagrange equations      97 100 101 498
Exponential map      132
Extended group      15 17 18 178 179 185
Extended Lie — Backlund group      461
Extended Lie — Backlund group in the plane      15 17 183 191
Extended Lie — Backlund group operator      188 202 247
Extended versus prolonged group      200
Exterior differential forms      59
Falkner — Skan boundary layers      305 325 357
Falkner — Skan boundary layers Falkner — Skan equation      307
Falkner — Skan boundary layers sink floss      310 312
Falkner — Skan boundary layers source flow      310
Falkner — Skan boundary layers velocity profiles      308
Falkner, V.M.      317
Falling dominos      52 53
Family of curves      56 131
Family of curves circles      131
Family of curves ellipses      165
Family of curves parabolas      63 457 466
Family of curves solution curves      167
Feynman, R.P.      xxxiii xl 4 11 32
Find Determining Equations      209 210 255 584 585 591 593 594 595 597 599
Fine scale motions      408 424
Finite form of a Lie group      132 163
Finite Lie — Backlund transformation      447 449
Finite transformation of first derivatives in the plane      15 193
Finite transformation of first partial derivatives      239
Finite transformation of higher derivatives in the plane      196
Finite transformation of second and higher partial derivatives      239 240
Finite transformation of second derivatives in the plane      195
First order linear ODE in n dimensions      62 160
First order linear PDE in n dimensions      81
First order ODEs      55 57 61 69 149 157 206
First order ODEs table of      158
First order PDEs      55 57 61 70 81
First order PDEs nonlinear      74
Flow in a diverging channel      325
Force free convection equation      275
Forsyth, A.R.      3 31 515 550
Foucault pendulum      119
Frames of reference      321 322 351 362 404
Frames of reference nonuniform translation, compressible flow      549
Frames of reference nonuniform translation, incompressible flow      321
1 2 3 4
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