Introduction to Symmetry AnalysisCambridge University Press, 23 sept. 2002 Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis 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. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries. |
Table des matières
XVI | 1 |
XVII | 3 |
XVIII | 4 |
XIX | 10 |
XX | 12 |
XXI | 13 |
XXII | 14 |
XXIII | 23 |
CLXVIII | 277 |
CLXIX | 279 |
CLXX | 281 |
CLXXI | 282 |
CLXXII | 284 |
CLXXIII | 291 |
CLXXIV | 293 |
CLXXV | 294 |
XXIV | 25 |
XXV | 29 |
XXVI | 31 |
XXVII | 33 |
XXVIII | 38 |
XXIX | 43 |
XXX | 44 |
XXXI | 47 |
XXXII | 50 |
XXXIV | 54 |
XXXV | 55 |
XXXVII | 56 |
XXXVIII | 57 |
XL | 59 |
XLI | 60 |
XLII | 62 |
XLIII | 65 |
XLIV | 68 |
XLV | 69 |
XLVI | 70 |
XLVII | 72 |
XLVIII | 73 |
XLIX | 74 |
L | 79 |
LI | 82 |
LII | 83 |
LIII | 84 |
LV | 85 |
LVI | 88 |
LVII | 90 |
LVIII | 91 |
LIX | 95 |
LX | 96 |
LXI | 98 |
LXII | 101 |
LXIII | 103 |
LXIV | 105 |
LXV | 108 |
LXVI | 119 |
LXVIII | 120 |
LXIX | 121 |
LXXI | 122 |
LXXIII | 123 |
LXXV | 125 |
LXXVI | 127 |
LXXVII | 128 |
LXXVIII | 130 |
LXXX | 132 |
LXXXII | 134 |
LXXXIII | 135 |
LXXXIV | 136 |
LXXXV | 137 |
LXXXVI | 138 |
LXXXVIII | 139 |
XC | 142 |
XCI | 145 |
XCIII | 148 |
XCIV | 149 |
XCVI | 152 |
XCVII | 155 |
XCVIII | 157 |
XCIX | 162 |
C | 166 |
CI | 172 |
CII | 174 |
CIII | 176 |
CV | 177 |
CVI | 178 |
CVII | 179 |
CVIII | 181 |
CX | 183 |
CXI | 184 |
CXII | 185 |
CXIII | 186 |
CXIV | 187 |
CXVI | 188 |
CXVII | 189 |
CXVIII | 190 |
CXX | 191 |
CXXI | 193 |
CXXII | 195 |
CXXIV | 197 |
CXXV | 198 |
CXXVI | 199 |
CXXVII | 200 |
CXXVIII | 201 |
CXXIX | 202 |
CXXX | 203 |
CXXXIII | 204 |
CXXXIV | 207 |
CXXXV | 208 |
CXXXVI | 213 |
CXXXVIII | 214 |
CXXXIX | 215 |
CXL | 216 |
CXLI | 217 |
CXLII | 219 |
CXLIII | 228 |
CXLIV | 230 |
CXLV | 231 |
CXLVI | 233 |
CXLVIII | 236 |
CXLIX | 237 |
CL | 238 |
CLII | 239 |
CLIII | 241 |
CLIV | 242 |
CLV | 243 |
CLVI | 245 |
CLVII | 247 |
CLIX | 248 |
CLX | 255 |
CLXI | 257 |
CLXII | 263 |
CLXIII | 269 |
CLXIV | 270 |
CLXV | 272 |
CLXVI | 273 |
CLXVII | 275 |
CLXXVI | 295 |
CLXXVII | 298 |
CLXXVIII | 299 |
CLXXIX | 301 |
CLXXX | 305 |
CLXXXI | 310 |
CLXXXII | 313 |
CLXXXIV | 317 |
CLXXXV | 318 |
CLXXXVII | 321 |
CLXXXVIII | 323 |
CLXXXIX | 325 |
CXC | 329 |
CXCI | 330 |
CXCII | 335 |
CXCIII | 353 |
CXCV | 357 |
CXCVI | 360 |
CXCVII | 361 |
CXCVIII | 362 |
CXCIX | 364 |
CC | 365 |
CCI | 369 |
CCII | 370 |
CCIII | 371 |
CCIV | 372 |
CCV | 375 |
CCVI | 382 |
CCVII | 384 |
CCVIII | 386 |
CCIX | 389 |
CCX | 390 |
CCXI | 391 |
CCXII | 392 |
CCXIII | 393 |
CCXIV | 395 |
CCXV | 397 |
CCXVI | 401 |
CCXVIII | 403 |
CCXIX | 404 |
CCXX | 405 |
CCXXI | 407 |
CCXXII | 408 |
CCXXIII | 410 |
CCXXIV | 413 |
CCXXV | 415 |
CCXXVI | 417 |
CCXXVII | 419 |
CCXXVIII | 420 |
CCXXIX | 422 |
CCXXX | 424 |
CCXXXI | 425 |
CCXXXII | 437 |
CCXXXIII | 438 |
CCXXXIV | 444 |
CCXXXV | 446 |
CCXXXVI | 447 |
CCXXXVII | 449 |
CCXXXVIII | 452 |
CCXXXIX | 453 |
CCXL | 457 |
CCXLI | 459 |
CCXLIII | 461 |
CCXLV | 462 |
CCXLVII | 464 |
CCXLVIII | 466 |
CCXLIX | 471 |
CCL | 474 |
CCLI | 478 |
CCLII | 479 |
CCLIII | 481 |
CCLIV | 496 |
CCLVI | 497 |
CCLVII | 498 |
CCLVIII | 499 |
CCLX | 500 |
CCLXI | 504 |
CCLXII | 511 |
CCLXIII | 512 |
CCLXIV | 513 |
CCLXV | 515 |
CCLXVI | 517 |
CCLXVIII | 519 |
CCLXIX | 521 |
CCLXX | 522 |
CCLXXI | 533 |
CCLXXII | 547 |
CCLXXIII | 548 |
CCLXXIV | 550 |
CCLXXV | 552 |
CCLXXVI | 553 |
CCLXXVII | 554 |
CCLXXVIII | 555 |
CCLXXXI | 558 |
CCLXXXII | 559 |
CCLXXXIII | 560 |
CCLXXXIV | 562 |
CCLXXXV | 563 |
CCLXXXVI | 564 |
CCLXXXVII | 567 |
CCXC | 568 |
CCXCII | 571 |
CCXCIV | 572 |
CCXCV | 578 |
CCXCVI | 579 |
CCXCVII | 580 |
CCXCVIII | 581 |
CCXCIX | 582 |
CCCI | 584 |
CCCII | 586 |
CCCIII | 587 |
CCCIV | 587 |
CCCV | 589 |
CCCVI | 590 |
CCCVII | 593 |
CCCVIII | 595 |
CCCIX | 597 |
CCCX | 600 |
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Expressions et termes fréquents
Bäcklund Bäcklund transformations Blasius equation boundary conditions boundary-layer Chapter characteristic equations coefficients constant contact condition contact transformation coordinates corresponding critical point curves defined depend determining equations differential equations differential function dilation group dimensional analysis dimensions dx³ example extended group finite first-order ODE flow fluid gradient group operator group parameter heat equation higher-order independent variables infinitesimal transformation integrating factor invariance condition Klein layer Lie algebra Lie group Lie series Lie-Bäcklund groups Lie-Bäcklund transformation linear mathematical mathematician motion Navier-Stokes equations nonlinear one-parameter partial derivatives phase portrait point groups problem result Reynolds number satisfy shown in Figure solution solvable Lie algebra solve Sophus Lie space symmetry analysis theory total differentiation trajectory turbulent velocity viscous y₁ zero ди др дув дх ду дхі მ მ
Fréquemment cités
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