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Nayfeh A.H. Ч Perturbation Methods
Nayfeh A.H. Ч Perturbation Methods

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Ќазвание: Perturbation Methods

јвтор: Nayfeh A.H.

јннотаци€:

The Method of Perturbations (asymptotic expansions) is an approximations technique for solving complicated problems in mathematics, engineering and physics involving nonlinear equations, variable coefficients and nonlinear boundary conditions. The purpose of this book is to present in a unified way an account of some of these techniques, pointing out their similarities, differences, and advantages, as well as their limitations.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1973

 оличество страниц: 425

ƒобавлена в каталог: 14.05.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Acoustic      77 78
Aerodynamic      110
Airfoil theory      98 99 235 303;
Airy's equation      312 336
Airy's functions      49 336 378
Algebraic equation      2 57 74 95 327
Algorithm      168 171 199 209
Algorithm for canonical systems      212Ч214
Algorithm, generalized      202Ч206
Algorithm, simplified      206Ч208
Anomaly      79
Aperiodic motion      189
Astrophysics      235
Asymptotic expansion      23 78
Asymptotic expansion of Airy's functions      337
Asymptotic expansion of Bessel's function      16
Asymptotic expansion, definition of      12
Asymptotic expansion, divergent      16
Asymptotic expansion, elementary operation on      18Ч19
Asymptotic expansion, uniform      17Ч19
Asymptotic expansion, uniqueness of      14 see also Asymptotic series
Asymptotic matching principle      see Matching
Asymptotic partitioning      327Ч331
Asymptotic sequence      12 14 16 18 19
Asymptotic sequence, factorial      12
Asymptotic sequence, fractional powers in      136 137
Asymptotic sequence, logarithms in      137 144
Asymptotic series      10Ч12
Asymptotic series, definition of      11
Asymptotic series, versus convergent series      15Ч16 see Asymptotic expansion
Attenuation      46 78
Averaging, generalized method of      168Ч171 191 211 223Ч225 231
Averaging, Krylov Ч Bogolinbov Ч Mitropolski, method of      174Ч179 183 194 211 212 223 224 246 248
Averaging, method of      159Ч227
Averaging, Struble's method of      171Ч174 176 183 194 223
Averaging, using, canonical variables      179Ч189
Averaging, using, Lagrangian      216Ч222
Averaging, using, Lie series and transforms      200Ч216
Averaging, van der Pol's method of      164Ч165 see also Smoothing
Averaging, von Zeipel transformation      189Ч200
Beam, vibration of      105 106 155 226 306
Bearing, slider      54 125Ч128
Bellman, equation of      22
Benard problem      77
Bending of, shells and tubes      54 353;
Benney's technique      38Ч42
Bernoulli's equation      83
Bessel functions      1 5 6 15 312 315 383
Bessel functions, asymptotic expansion of      16 312Ч314 329Ч331
Bessel functions, integral representation of      16 314
Bessel functions, zeros of      21
Bethe Ч Salpeter equation      372
Blunt body problem      99
Boltzmann's equation      236
Born approximation      362
Born expansion      308 361Ч367 373
Born expansion, renormalization of      367Ч372
Boundary conditions, loss of      31 34 37 38 54 111 114 122
Boundary conditions, transfer of      27
Boundary layer      18 23 79 111 112 147 233
Boundary layer, location of      114Ч116 122
Boundary layer, Prandtl      34
Boundary layer, problem with two, s      128Ч133
Boundary layer, stability of      353
Branch point      82
Bretherton's equation, exercises involving      227 306
Bretherton's equation, treated, by method of multiple scales      266Ч269 298Ч300
Bretherton's equation, treated, by variational approach      217Ч221
Bretherton's equation, wave-wave interaction for      219Ч221 266Ч269
Brownian motion      236
Buckling      233
Canonical equations      180 199
Canonical, averaging, variables      179Ч189
Canonical, Jordan, form      327
Canonical, mixed, variables      199
Canonical, system      190 201
Canonical, transformation      181 187 191
Canonical, variables      181 183 184 195 202 216 224
Caustic      234 375Ч380
Change      111 113
Change of characteristics      89 see also Sharp change; Type change of
Characteristic exponent      58 62 66
Characteristic, parameters      89 94
Characteristic, wave speeds      91
Characteristics, expansion in terms of      57 86Ч94 303
Characteristics, method of      374
Circuit, electronic      see van der Pol oscillator
Cluster expansions      363
Compatability relationship      217 222
Composite expansion      114 144 384 385
Composite expansion for earth-moon-spaceship problem      139
Composite expansion for equation with variable coefficients      125
Composite expansion for simple example      121Ч122
Composite expansion for slider bearing      128
Composite expansion for thermoelastic waves      136
Composite expansion for unsymmetrical bending of plates      133
Composite expansion, construction of      121
Composite expansions, applied to turning point problems      348Ч350
Composite expansions, method of      144Ч154 317 318
Composite solution      113
Conservation form of equations      226
Coordinate, optimal      50Ч51
Coordinate, parabolic      79
Coordinate, perturbations      1 4Ч7 21 309Ч314 379
Coordinate, role of, systems      23 49Ч52 54 380
Correlation      363
Cosmological expansion      233
Cycle, limit      35
Cylinder, a solid, expanding      83Ч86
Cylinder, elliptic      346
Cylindrical, functions      358 378 380
Cylindrical, jet      99
Degenerate      72 74
DerivativeЧexpansion procedure      302
DerivativeЧexpansion procedure, applications of      243Ч269
DerivativeЧexpansion procedure, description of      230 236Ч240
DerivativeЧexpansion procedure, limitations of      269Ч270 see also Multiple scales method
Detuning      250
Diagram      366 367
Diagram, bare      364
Diagram, connected      370 371 372
Diagram, double      365
Diagram, dressed      365
Diffraction      346 380
Diffusion equation      38
Dirichlet problem      38
Discontinuity      see Singularity
Dispersion relationship      178 217 218 219 220 222 227 266 301
Dispersive waves      78 234 303
Dispersive waves, long nonlinear      38Ч42 see also Bretherton's equation; Klein Ч Gordon equation; Thermo-elastic waves; Wave-wave interaction
Divisor, small      196
Domain, effect of, on nonuniformity of expansions      38 42
Domain, infinite      24Ч31
Duffing equation      50 51
Duffing equation with slowly vary coefficients      286
Duffing equation, exercises involving      54 104 105 223 224 304
Duffing equation, straightforward expansion for      24Ч25
Duffing equation, treated, by averaging using canonical variables      182Ч183
Duffing equation, treated, by derivative-expansion procedure      243Ч245
Duffing equation, treated, by generalized method of multiple scales      286Ч291
Duffing equation, treated, by Krylov Ч Bogoliubov method      167
Duffing equation, treated, by Krylov Ч Bogoliubov Ч Mitropolski method      175Ч176
Duffing equation, treated, by Lindstedt Ч Poincare method      58Ч60
Duffing equation, treated, by renormalization      95Ч96
Duffing equation, treated, by Struble's method      171Ч174
Duffing equation, treated, by two-variable expansion procedure      271Ч273
Duffing equation, treated, by von Zeipel's procedure      192Ч194
Dyson equation      371 381
Earth-moon-spaceship problem      233 302 303
Earth-moon-spaceship problem, exercises involving      53 107
Earth-moon-spaceship problem, illustrating limitations of method of strained coordinates      102Ч103
Earth-moon-spaceship problem, straightforward expansion for      43Ч45
Earth-moon-spaceship problem, treated, by Lighthill's technique      82Ч83
Earth-moon-spaceship problem, treated, by method of composite expansions      153Ч154
Earth-moon-spaceship problem, treated, by method of matched asymptotic expansions      137Ч139
Earth-moon-spaceship problem, treated, by method of multiple scales      295Ч298
Eccentricity      64 233 346
Edge layer      111
Eiconal equation      374 377 379
Eigenvalue      56
Eigenvalue problem, linear      68Ч71
Eigenvalue problem, quasilinear      71Ч76
Elastic      46 58 90 353
Elastic waves      89Ч94
Elliptic equation      37 42 98 189 234 303 360
Energy level      56 58
Entropy layer      79
Euler Ч Lagrange equation      216 217 218 220 222
Faa de Bruno operators      192
Feynman diagrams      308 361Ч372
Flight mechanics      233
Floquet theory      60 62 64 66
Flow past a sphere, exercise involving      158
Flow past a sphere, straightforward expansion for      28Ч31
Flow past a sphere, treated by method of matched asymptotic expansions      139Ч144
Flow through a channel      54 56 216
Flow, down an inclined plane      38Ч42 99
Flow, hypersonic      79
Flow, jet      99
Flow, past a body      33Ч34 113
Flutter      234
foci      253
Fokker Ч Planck equation      235 381
FOURIER      45 167 178
frequency      56 58 96 165 252
Fresnel diffraction      380
Frobenius, method of      5 310
Gauge, function      7 8
Gauge, transformation      232
Gaussian      363 367 369 372
Generalized expansion      see Composite expansion
Generalized method of averaging      see Averaging method
Generalized vector      179
Generalized version of method of multiple scales, applications of      276Ч302
Generalized version of method of multiple scales, description of      232 241Ч243
Generalized version of method of multiple scales, limitations of      302Ч303
Generating function      181 184 189 190 192 195 196 200 202 215
Generating vector      201
Geometrical optics      308 361 374Ч377 379
Geophysics      110
Graetz problem      384
Green's function      362 364 380
Green's function, double      364
Group velocity      179 219 220 267 299
Hamilton Ч Jacobi equation      181 182 183 186 190 199
Hamiltonian      223 224 225
Hamiltonian for Duffing equation      182
Hamiltonian for Mathieu equation      184
Hamiltonian for swinging spring      186
Hamiltonian, definition of      180
Hamiltonian, transformation of, using Lie transforms      202 212Ч216
Hamiltonian, transformation of, using von Zeipel procedure      189Ч200
Harmonic balance      218
Harmonic resonance      219Ч221 234 262Ч269
Harmonic wave      76
Heat      45 79 84 156 342 384
Heat, problem for, equation      150Ч152
Helmholtz equation      234
Hill's equation      60
Hopf equation      381
Hydraulic jump      89
Hyperbolic equation      37 42 57 99 379.
Inclined plane      see Flow down
Indicial equation      311
Induction      13
Infinite domain, as a source, of nonuniformity      23Ч31 229
Infinite domain, as a source, of uniformity      38 42
Inhomogeneous      361
Inhomogeneous, problems with turning points      352Ч359
Initial, boundary value problem for heat equation      150Ч152
Initial, layer      23
Inner and our expansions      see Matched asymptotic expansions method
Inner expansion      110 112 114 119 145 146 148
Inner expansion for bending of plates      129Ч132
Inner expansion for earth-moon-spaceship problem      139
Inner expansion for equation with variable coefficients      122Ч124
Inner expansion for simple example      117Ч118
Inner expansion for slider bearing      127
Inner expansion for thermoelastic waves      134Ч135
Inner expansion for turning point problems      336
Inner expansion, definition      117Ч118
Inner limit      112 118 119 129 131 139
Inner region      113 122 146 153
Inner solution      112 113
Inner variables      119 120 121 144 149 153 154
Inner variables, choice of      114Ч116 122Ч124 126Ч127 134Ч135 137Ч138
Inner variables, generalized      145
Instability      78 269.
integral      10 11 12
Integral of motion      24 199
Integral, differential equation      18
Integral, equation      370 380
Integral, relations      99
Intermediate limit      119
Intermediate matching      see Overlapping
Jacobi elliptic functions      189
Jacobian matrix      202
Jerky oscillations      34
Jordan, form      327
Jordan, matrix      327
Josephson tunnel      221
Kamel's algorithm      171
Kamel's method      224
Kelvin Ч Helmholtz      77 235
Kernel      370
Kiylov Ч Bogolinbov, method of      165Ч168
Klein Ч Gordon equation      175 234
Klein Ч Gordon equation, exercises involving      105 226
Klein Ч Gordon equation, treated, by averaging using Lagrangian      221Ч222
Klein Ч Gordon equation, treated, by Krylov Ч Bogoliubov Ч Mitropolski method      178Ч179
Klein Ч Gordon equation, treated, by method of multiple scales      301Ч302
Klein Ч Gordon equation, treated, by method of strained parameters      76Ч77
Kruskal's technique      168 191
Krylov Ч Bogoliubov technique      165Ч168 223
Krylov Ч Bogoliubov Ч Mitropolski technique      174Ч179 183 194 211 212 223 224 246 248 303
Lagrange equations      179 180
Lagrangian      179
Lagrangian for Bretherton's equations      217
Lagrangian for Klein Ч Gordon equation      221
Lagrangian for swinging spring      186
Lagrangian, averaging using      216Ч222 301
Lame coefficients of elasticity      45 90
Laminar      39 54
Landau, equation      382
Landau, symbols      8 9
Langer's transformation      308 346 384
Langer's transformation for first-order turning point problems      339Ч341
Langer's transformation for generalization of      341Ч342
Langer's transformation, successive      350
Latta's technique      144Ч154
Layer      23 79 111;
Libration points      see Stability of elliptic triangular points
Lie series and transforms      171 199 200Ч216 223 225 303
Lie triangle      205 206
Lighthill's technique      57 77Ч95
Lighthill's technique, exercises involving      107 108
Lighthill's technique, limitations of      79 98Ч100 107 109
LIMIT      7
Limit, cycle, point, or solution      35 99 109
Limit, distinguished      336
1 2 3
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