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Murray J.D. — Asymptotic Analysis
Murray J.D. — Asymptotic Analysis



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Название: Asymptotic Analysis

Автор: Murray J.D.

Аннотация:

From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics. The book presents a balanced view of the methods and their usefulness: integrals on the real line and in the complex plane which arise in different contexts, and solutions of differential equations not expressible as integrals. Murray includes both historical remarks and references to sources or other more complete treatments. More useful as a guide for self-study than as a reference work, it is accessible to any upperclass mathematics undergraduate. Some exercises and a short bibliography included. Even with E.T. Copson's Asymptotic Expansions or N.G. de Bruijn's Asymptotic Methods in Analysis (1958), any academic library would do well to have this excellent introduction." (S. Puckette, University of the South) Choice Sept. 1984


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 180

Добавлена в каталог: 10.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Airy, G.B.      54
Airy, G.B., equation      54 70 115 133
Airy, G.B., function asymptotic expansions      60 61 69 70 134
Airy, G.B., functions      54 133
Airy, G.B., integral      57
Asymptotic, equivalence      4
Asymptotic, expansion      5
Asymptotic, expansion (definition)      12
Asymptotic, expansion (uniqueness)      12
Asymptotic, matching process      133
Asymptotic, power series      13
Asymptotic, sequence      11
Bessel, equation      55 105 133
Bessel, function asymptotic forms      65 78 105 137
Bessel, functions      61
Bleistein, N.      51
Burkill, J.C.      101
Carrier, G.F.      51 161
Cauchy — Riemann equations      43
Chester, C.      51
Cohen, D.S.      138 150 161
Cole, J.D.      2 138 159 161
Composite expansion      149
Contour integral solutions      55
Convergent power series      4
Copson, E.T.      19 161
de Bruijn, N.G.      16 161
de Laplace, integral      21
de Laplace, method      28
de Laplace, P.S.      29
Debye, P.      40
Differential equations      99
Differential equations, asymptotic solutions involving a parameter      111
Differentiation of asymptotic series      16
Dingle, R.B.      161
dispersion relation      80
Divergent series      8
Dominant Term      13
Erdelyi, A.      99 161
Error function      20 27
Exponential function, complex argument      9
Exponential function, real argument      6 20
Fourier transform      86
Fourier transform, asymptotic expansions      90 91
Friedman, B.      51
Frobenius method      101
Gamma function, analytic continuation      54
Gamma function, complex argument      51
Gamma function, real argument      19 37
Garabedian, P.R.      127
Gauge function      3
Green, G.      111
Group velocity      84
Handelsman, R.A.      51
Hankel function      62
Hankel function, asymptotic forms      65
Hankel integral      68
Horn, J.      111
Ince, E.L.      101
Inner solution      145
Integration, by parts method      19
Integration, of asymptotic series      15
Intermediate, region      141
Intermediate, variable      148
Jeffreys, B.S.      81
Jeffreys, H.      51 81 161
Kelvin, Lord      72
Kevorkian, J.      138 159 161
Krook, M.      51 161
Lamb, H.      84
Laplace transform      86 96
Laplace transform, asymptotic expansion      97
Lighthill, M.J.      81
Limit cycle      158
Liouville equation      111
Liouville equation, asymptotic solutions      114
Liouville, J.      111
Matched asymptotic procedure      118
Murray, J.D      138 161
Nayfeh, A.H.      138 159 161
Nayfeh, nonlinear      138 159
Nayfeh, nonsingular solution      138 159
O-order      3
Ockendon, J.R.      121
Order notation      2
Outer solution      145
O’Malley, R.E.      138 159 161
Parabolic cylinder functions      108
Parabolic cylinder functions, asymptotic forms      109
Pearson, C.      51 161
Poincare, H.      2 12 159
Power series      5
Power series, differentiation      16
Power series, integration      15
Regular perturbation      141
Riemann, B.      40
Saddle point      43
Saddle point, method      40
Schroedinger equation      127
Schroedinger equation, short wave length solutions      127
Schroedinger equation, spherically symmetric form      131
Secular terms      121 152
Singular, perturbation theory      99 122 138
Singular, region      141
Singular, solution      145
Singularity      100
Singularity, irregular      101
Singularity, regular      100
Sneddon, I.N.      86
Stationary phase      72
Steepest descents      40
Stirling’s formula      38
Stokes, G.G.      72
Stretching transformation      143
Transition point      128 131
Two time method      153
Ursell, F.      51
van der Pol equation      156 160
Van Dyke, M.      2 138
Wasow, W.      99 161
Watson, G.N.      16 21 161
Watson, lemma      19
Wave, frequency      80
Wave, group velocity      84
Wave, high frequency oscillations      125
Wave, motion      79
Wave, number      80
Wave, slowly varying wave train      82
Wave, speed      80
Whitham, G.B.      84
Whittaker, E.T.      16
WKB method      111
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