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De Bruijn N.G. — Asymptotic methods in analysis
De Bruijn N.G. — Asymptotic methods in analysis

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Название: Asymptotic methods in analysis

Автор: De Bruijn N.G.

Аннотация:

This book arose from a course of lectures given during the
academic year 1954/55 at the Mathematical Centre, Amsterdam,
repeated in 1956/57 in a course at Eindhoven, organized by the
same institution. Its purpose is to teach asymptotic methods by
explaining a number of examples in every detail, so as to suit
beginners who seriously want to acquire some technique in attacking
asymptotic problems.
Although asymptotics is by no means a new field, only in recent
times have special courses and books been devoted to it. The
reason may be that today university courses in analysis are
condensed in favour of modern mathematics. The effect is that analytic
techniques are not so widespread as they used to be. On the other
hand there are so many questions of an asymptotic nature both in pure
and applied mathematics, that we cannot afford to neglect the
subject. Therefore it seems desirable to give a separate training in
asymptotics to those who have only a general knowledge of analysis.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second edition

Год издания: 1961

Количество страниц: 211

Добавлена в каталог: 22.03.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\approx$      11
Abel's equation      160
Abel, Abelian theorems      139
Alternating sums      49
Argument of the axis of a saddle point      84
ARMAC      174
Asymptotic behavior      10
Asymptotic equivalence      10
Asymptotic expansion      11
Asymptotic series      11
Asymptotics      1
Axis of a saddle point      84
Bachmann      3
Bernoulli numbers      41 158
Bernoulli polynomials      41
Bessel function      54 193
Boas      174
Boole sum formula      51
Bounded variation      53
Class partitions      102
Closed path theorem      82
Conformal mapping      124
Continuous iteration      153 160
Contribution of a saddle point      88
Copson      167
Crossing of a saddle point      81
Debye      77
Differentiation of an asymptotic formula      15 17 139
Direct asymptotics      134
Dixon      72
Euler      47
Euler — Maclaurin sum formula      40 109
Euler's constant      58
Exponential integral      13
Exponentially small      44
Fourier series      52
Functional equations of gamma function      48
Gamma function      46 69 119
Gauss' factorial      110
hankel      101
Hardy      138
Hermite polynomials      45
Implicit functions      21
Indirect asymptotics      134
Integration of an asymptotic formula      17
Iteration      13 28 31 148 193
Karamata      143
Koenigs      153
Kronecker symbol      75
Lagrange inversion formula      22
Landau      3
Laplace      1 60 77
Lebesgue integrals      100
Little wood      138
Mountaineering      80
Multiple integrals      71
Neumann series      192
Newton      30 31
Numerical analysis      18 174
Numerical equations      30
o      3
Oscillatory      189
Perturbations      96
Poincare      11
Poisson's sum formula      52
Power series      14
Prime numbers      2 57 59
Range of a saddle point      91
refinement      7
Riccati      177
Riemann      77
Riemann's zeta function      40 42
Roots of equations      30
Rouche      26 122
Saddle point      80
Schroeder      152 160
Stability      183
Stationary phase      84
Steepest descent      85 86
Stirling's formula      1 42 46 70 127
Summation by parts      56
Tauber      138
Tauber, Tauberian theorems      139
Theta functions      45
Uniformity with respect to a parameter      7
Unstable      184
Van Wijngaarden      175
Volume of unit sphere      72
Weierstrass      145
Wielandt      144
Wintner      196
Zeta function      40 42
~      10
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