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| Hinch E.J. — Perturbation Methods |
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| Предметный указатель |
 22
Accumulation of small effects 116
action 129
Additive extraction 149
Adiabatic invariant 129
Airy function 34 99 131
Algebraic equations 1
Amplitude drift 116
Asymptotic approximation 20
Asymptotic sequence 21
Asymptotic, why? 23
Asymptoticne8s 19
Averaged lagrangian 141
Bessel functions 37
Boundary layer 52 55
Boundary layer, where? 63
Breakdown of asymptoticness 98 118
Cancellation of oscillations 30 31
Channel flow 47
Characteristics 110
Child’s swing 120
Composite approximations 65 73 107
Composite material 126
Conformal map 88
Continued fractions 152
Convergence 19
Convergence, improved 144 147
Convergence, why 14
Differentiating approximations 23
Diffusion-advection equation 123
dispersion relation 138
Distinguished limits 62
Domb — Sykes plot 145
Drift of amplitude 116
Duffing’s oscillator 108
Effective diffusivity 125
Effective heat conductivity 127
eigenvalue problems 15 50
Eigenvalues, degenerate roots 18
Eigenvalues, multiple roots 17
Eigenvalues, second order 16
Electrical capacity 42 47 87
Elliptic integral 42 146
Equipartion of energy 143
Equivalent radius 88
Error function 19 24 26 28
Euler transformation 149
exercises 4 8 11 13 18 21 24 29 37 42 45 47 50 58 59 60 63 65 67 73 77 86 92 96 108 120 122 123 130 134 140 141 146 147 151 154
Expansion method 3
Expansion sequence 9
Exponential integral 29 70
Exponentially small terms 57 135
Fast time scale 117
Fourier series 29
Gearing 40
Geometric optics 141
Global considerations 30
Global contributions 37
Group velocity 138
Heat transfer 86
Homogenised media 126
Improved convergence 144 147
Inertial flow past a cylinder 50
Inner approximation 55
Instability of the mathieu equation 120
Integrability condition 118
Integral equation 42 90
Integrals 27
Integration by parts 29
Intermediate equation 62
Intermediate limits, all 71 77 81
Intermediate variable 57
Intrinsic frequency 139
inversion 147
Iteration and expansion 1
Iterative method 2
Jumping order 57 61 72 81
Lagrangian, averaged 141
Laplace’s method 30
Legendre functions 37 133
Limit cycle 97
Local considerations 32
| Local frequency and wavenumber 137
Logarithmico-exponential functions 21
Logarithms 12 41 43 67
Long slender body 42
Matched asymptotic expansion 52
Matching 57
Mathieu equation instability 120
Method of strained coordinates 102
Moon space ship problem 93
Moving medium 139
Multiple scales, method 116
Multiplicative extraction 149
Non-integral powers 8
Non-local contributions 37
Non-uniform limits 54
Numerical use of diverging series 24
Numerical values xii 90
Orbit about earth and moon 92
Orbit of satellite 122
Ord() 6
Outer approximation 54
Pade approximants 151
Parametric excitations 120
Parametric expansions 25
Patching 59
Pattern of signs 145
Period of van der pol oscillation 101
Poincar6 expansions 25
Potential outside a near sphere 46
Radius of convergence 144
Ray theory 140
Reflected wave 136
Regular perturbations 4 46
Rescaling 6 28 38 55 68
Resonant forcing 118
Riemann invariants 111
Rotating self-gravitating mass 48
Saddle points 30
Schrodinger’s equation 133
Secularity condition 118
Shallow water waves 110
Shanks transformation 150
Simplest choice 105
Singular perturbations 4 52 102
Slender body theory 87
Slender body, axisymmetric potential flow 90
Slender body, electrical capacitance 87
Slow accumulation 116
Slow time scale 117
Slow viscous flow past a cylinder 84
Slow viscous flow past a sphere 81
Slowly varying waves 137
Solubilty condition 118
Splitting a range of integration 39
Stationary phase 30
Steepest descents 30
Stirling’s formula 33
Stokes phenomenon 26 132
Strained co-ordinate 102 119
Stretched co-ordinate 55
Stretching, choice 60
Substituting asymptotics approximations 22
Subtracting off 38
Super slow time scale 119
Switchback 71
Taking a root 148
Transfer of boundary condition 46
Transition phase 99
Turning points 131
Uniqueness of asymptotic approximation 21
van der Pol oscillator xi 97 116
Van dyke’s matching rule 58
Van dyke’s matching rule, failure 72
Water waves 50
Watson’s lemma 27
Wave action 139 143
Wave breaking 114
Wave crests, conservation 141
Wave kinematics 141
Wave scattering 87
Widely separated particles 92
Wkbj approximation 127
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