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Hinch E.J. — Perturbation Methods
Hinch E.J. — Perturbation Methods

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Название: Perturbation Methods

Автор: Hinch E.J.

Аннотация:

In this book the author presents the theory and techniques underlying perturbation methods in a manner that will make the book widely appealing to readers in a broad range of disciplines. Methods of algebraic equations, asymptotic expansions, integrals, PDEs, strained coordinates, and multiple scales are illustrated by copious use of examples drawn from many areas of mathematics and physics. The philosophy adopted is that there is no single or best method for such problems, but that one may exploit the small parameter given some experience and understanding of similar perturbation problems. The author does not look to perturbation methods to give quantitative answers but rather uses them to give a physical understanding of the subtle balances in a complex problem.


Язык: en

Рубрика: Математика/Анализ/Асимптотические методы, Теория возмущений/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 160

Добавлена в каталог: 26.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\epsilon \searrow 0$      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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