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| Ïîèñê ïî óêàçàòåëÿì |
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| Holmes M.H. — Introduction to Perturbation Methods |
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| Ïðåäìåòíûé óêàçàòåëü |
 symbol 6
 symbol 6
 symbol 7 9
Acherberg — O'Malley resonance 81
Acoustic thermometer 207
Adiabatic explosion temperature 76
Air flow, supersonic 49
Airy functions 175 297—298
Airy functions, expansions of 298—299
Airy functions, graph of 298
Airy's equation 174 297
Arithmetic mean 232
Asymptotic approximations of Asymptotic approximations, algebraic equations 18—22
Asymptotic approximations, defined 7
Asymptotic approximations, differentiating 14
Asymptotic approximations, ideas underlying 13 47
Asymptotic approximations, of differential equations 26—31
Asymptotic approximations, of integrals 305—307
Asymptotic approximations, of transcendental equations 21—22
Asymptotic approximations, uniform 37—42
Asymptotic expansions 1
Asymptotic expansions, coefficients of 10
Asymptotic expansions, concept introduced 13—14
Asymptotic expansions, defined 9
Asymptotic expansions, differentiating 14—15
Asymptotic expansions, divergent 12
Asymptotic expansions, finding 9—11
Asymptotic expansions, integrating 15
Asymptotic expansions, manipulating 14—15
Asymptotic expansions, matched see “Matched asymptotic expansions”
Asymptotic expansions, nonuniform 39
Asymptotic expansions, of eigenvalues 25—26 67 122 164 170 180 219—220
Asymptotic expansions, well ordered 19
Asymptotic sequences 9
Asymptotic series, accuracy versus convergence of 12—14
Asymptotic stability 257 258
Asymptotically equal functions 11
Asymptotically stable orbit 284
Asymptotically stable solutions 258
Attraction, basin of 250
Attractive solutions 258
Averaging in method of homogenization 243—244
Averaging procedure, properties of 230
Bachmann — Landau symbols 4
Balancing terms 19
Basin of attraction 250
Basis functions 9
Beam equation 171 189
Beam equation, damped 137
Beam equation, nonlinear 131 137 278
Bessel's equation 171
Bifurcating solutions, schematic of structure of 254
Bifurcation and stability, introduction to 249—291
Bifurcation and stability, introductory example 249—251
Bifurcation of periodic solutions 281—285
Bifurcation parameter 250
Bifurcation point 250 251
Bifurcation point, analysis of 251—255
Bifurcation, degenerate 284—285
Bifurcation, global 277
Bifurcation, imperfect 263
Bifurcation, pitchfork 250
Bifurcation, steady-state 249
Big oh 4
Big oh, two meanings of 20
Binomial expansion 3
Biological switching mechanism 270
Bistability 126 264
Bloch expansion 240
Boundary layers 50—51
Boundary layers, matching and 52 64—65 89
Boundary layers, multiple 62—65
Boundary layers, multiple scales and 132—133
Boundary layers, parabolic 90—91
Boundary-layer coordinate 50 63 87
Boundary-value problems, FORTRAN program for solving 309—312
Boundary-value problems, nonlinear, numerical solution of 309—312
Boussinesq equation 149
Breathers 158 281
Brusselator 293
Buckled states 278
Buckling 271—272
Buckling loads 260
Burgers' equation 91
Burgers' equation, solutions of 95
Caustics 200
cells 234—235
Cells, averages of functions over 236—237
Cells, in plane 235
Characteristic coordinates, introducing 198
Coefficients, slowly varying 117—120
Cole — Hopf transformation 95
Composite expansion 54—55 56 61 63—64 72 80 89 101
Computing, symbolic 43—45
Confluent hypergeometric functions 81 299—302
Connection formulas 176
Convergent asymptotic expansions 12
Corner layers 77—81
Corner region 78
Corner-layer expansion 266—267
Cutoff frequency 196
Darcy's law 245
Debye — Huckel theory 30
Degenerate bifurcation 284—285
Difference equations, boundary layers and 98—102
Difference equations, multiple scales and 153—155
Difference equations, WKB and 212—218
Differential equations, approximate solutions of 1
Differential equations, asymptotic approximations of 26—31
Differential equations, homogenized 228
Differential equations, ordinary, systems of 287—291
Differential-difference equations 75
Diffusion, nonlinear 144—148
Diffusivity tensor 248
Dirichlet problem, inhomogeneous 234
Discrete WKB method 212—218
Disproportionate length scales 225
Dissipation function 136 186
Distinguished limit 51
Divergent asymptotic expansions 12
Divergent series, summability of 14
Dual-mode sorption model 246
Duffing's equation 35 249
Duffing's equation, forced 123 128
Effective coefficients 228
Eigenvalues of matrix 23
Eikonal equation 163
Elliptic equations 84—91
energy equation 136 186 190
Energy methods 186—188
Energy methods, wave propagation and 185—188
Energy, total 187
Euler buckling load 263
Exchange of stability 257
Expansion, composite 54—55
Exponential functions, transcendentally small 11
Exponentially small functions 9
Expression swell, intermediate 44
Extension theorem, Kaplun's 53
Fast dynamics 264—265
Fast length scale 225
Fisher — Wright — Haldane model 158
Fisher's equation 145 278
Flow, porous 241—245
Fokker — Planck equation 188
Forced motion near resonance 123—127
Fredholm alternative theorem 191 273
Fredholm integral equation 33
Functions, asymptotically equal 11 39
Functions, averages of, over cells 236—237
| Functions, transcendentally small 5
Functions, well-ordered 9
Gauge Functions 9
Geometric mean 232
Ginzburg — Landau equation 278
Global asymptotic stability 257
Global bifurcation 277
Hamiltonian function 107 136
Harmonic mean 228 230
Harmonic resonance 127
Helmholtz equation 198
hessian 287
Hidden variables 239
Higher-order turning points 302—303
Homogenization 223
Homogenization procedure 236—237
Homogenization, method of 223—245
Homogenization, method of, averaging in 243—244
Homogenization, method of, introductory example 224—231
Homogenization, method of, multidimensional problem 234—239
Homogenization, method of, reduction using 242—243
Homogenization, method of, with nonlinear equations 231
Homogenized coefficients 228
Homogenized coefficients, substructure and 237
Homogenized differential equations 228
Hopf bifurcation 255 284
Hurwitz polynomial 291
Hypergeometric equation 299
Hypergeometric functions, confluent 81 299—302
Ignition period 76
Imperfect bifurcation 263
Implicit function theorem 251
Inhomogeneous Dirichlet problem 234
Initial-layer expansion 266
Inner solution 53
Inner-inner layer 65
Instability 257
Integrals, asymptotic approximations of 305—307
Interior layer 68—73
Interior layer, matching and 69—72
Interior-layer coordinate 70 92
Interior-layer expansion 267—268
Intermediate variables 53
Intrinsic phase average 245
Kaplun's extension theorem 53
Kaplun's hypothesis on domain of validity 53
Kepler's equation 24—25
Klein — Gordon equation, nonlinear 138 142 281
Kolmogorov — Petrovsky — Piskunov (KPP) equation 145 278
Korteweg — de Vries (KdV) equation 149
Kummer's function 299—300
Kuramoto — Sivashinsky equation 279
l'Hospital's rule 4
Lagrangians, averaged 189
Landau symbols 4
Langmuir — Hinshelwood model 75
Laplace's approximation 306
Layer analysis, matching and 79—80
Least-squares problem 26
Length scales, disproportionate 225
Liebnitz's rule 197
Lindstedt's method 111
Linear stability theory 249
Linear wave propagation 139—141
Linearized stability 255—259
Linearized stability analysis 274—275
Liouville's equation 29
Little oh 4
Logistic equation with delay 286
Lyapunov — Schmidt method 252
Maclaurin series 3
Macroscale 225
Maintained vibrations 269—270
Maple commands for projectile problem 45
Matched asymptotic expansions 39 47—102
Matched asymptotic expansions, introductory example 48—57
Matching, boundary layers and 52 64—65
Matching, corner layer analysis and 79—80
Matching, importance of 56
Matching, interior layer and 69—72
Matching, overlap domain and 53
Matching, transition region and 175—176
Materials from multiple constituents 223
Mathieu's equation 121 261
Matrix perturbation problems 25—26
Matrix, eigenvalues of 23
Matrix, pseudo-inverse of 26
Maxwell's fisheye lens 206
Mercury's perihelion 128
Michaelis — Menten reaction scheme 59
Microscale 225
Microvoids 246
Mixture theory 245
Mixtures, rule of 233
Morse oscillator, forced 130
Multiple boundary layers 62—65
Multiple constituents, materials from 223
Multiple scales 105—155
Multiple scales, boundary layers and 132—133
Multiple scales, characteristic coordinates and 140 143
Multiple scales, difference equations and 153—155
Multiple scales, first-order systems and 116—117
Multiple scales, for traveling waves 139—141
Multiple scales, history of 105
Multiple scales, introductory example 106—113
Multiple scales, minimum error, principle of 112
Multiple scales, three time scales 110
Multiple solutions of nonlinear equations 70
Multiple-scale expansion 108—110
Negative damping 258
No-slip condition 241
Nonlinear boundary-value, problems, numerical solution of 309—312
Nonlinear diffusion 144—148
Nonlinear geometric optics method 167
Nonlinear wave equation 142—144
Nonlinear waves 142—148
Nonlinear WKB method 167
Nonuniform asymptotic expansions 39
Numerical solution of nonlinear boundary-value problems 309—312
Order symbols 4—6
Ordinary differential equations, systems of 287—291
Outer expansion 55
Outer scale 53
Outer solution 49—50 62 68 78 85 91 265
Parabolic boundary layers 90—91
Parabolic equations (PE) 91—94
Parabolic equations (PE), standard two-dimensional 209—211
Parabolic wave approximations 207—211
Paraxial approximation 209
Paul trap 115 142
Pe see “Parabolic equations”
Pendulum 114 121 262—263
Pendulum, elastic 294
Pendulum, forced 129 131
Pendulum, inverted 261—262
Periodic solutions, bifurcation of 281—285
Periodic substructure 231 234—239
Permeability tensor 245
Perturbation problems, matrix 25—26
Perturbation problems, regular 26
Perturbation problems, singular 48
Phase average 245
Phase fronts 198
Pitchfork bifurcation 250
Poincare — Andronov — Hopf bifurcation theorem 291
Poisson — Boltzmann equation 29
Porous flow 25 241—245
Power series functions, generalization of 9
Primary resonance 127
Projectile problem 1—3 27—28
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