翻訳と辞書 Words near each other ・ Inverse Faraday effect ・ Inverse filter ・ Inverse filter (disambiguation) ・ Inverse floating rate note ・ Inverse function ・ Inverse function theorem ・ Inverse functions and differentiation ・ Inverse Galois problem ・ Inverse gambler's fallacy ・ Inverse gas chromatography ・ Inverse Gaussian distribution ・ Inverse hyperbolic function ・ Inverse image functor ・ Inverse iteration ・ Inverse kinematics ・ Inverse Laplace transform ・ Inverse limit ・ Inverse magnetostrictive effect ・ Inverse mapping theorem ・ Inverse matrix gamma distribution ・ Inverse mean curvature flow ・ Inverse method ・ Inverse Mills ratio ・ Inverse multiplexer ・ Inverse Multiplexing for ATM ・ Inverse number ・ Inverse parser ・ Inverse Phase ・ Inverse photoemission spectroscopy ・ Inverse polymerase chain reaction Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Inverse Laplace transform ： ウィキペディア英語版 Inverse Laplace transform In mathematics, the inverse Laplace transform of a function ''F''(''s'') is the piecewise-continuous and exponentially-restricted real function ''f''(''t'') which has the property: :$\backslash mathcal\backslash (s)\; =\; \backslash mathcal\backslash (s)\; =\; F(s),$ where $\backslash mathcal$ denotes the Laplace transform. It can be proven that, if a function ''F''(''s'') has the inverse Laplace transform ''f''(''t''), then ''f''(''t'') is uniquely determined (considering functions which differ from each other only on a point set having Lebesgue measure zero as the same). This result was first proven by Mathias Lerch in 1903 and is known as Lerch's theorem. The Laplace transform and the inverse Laplace transform together have a number of properties that make them useful for analysing linear dynamic systems. ==Mellin's inverse formula== An integral formula for the inverse Laplace transform, called the ''Mellin's inverse formula'', the ''Bromwich integral'', or the ''Fourier–Mellin integral'', is given by the line integral: :$f(t)\; =\; \backslash mathcal^\; \backslash (t)\; =\; \backslash mathcal^\; \backslash (t)\; =\; \backslash frac\backslash lim\_\backslash int\_^e^F(s)\backslash ,ds,$ where the integration is done along the vertical line Re(''s'') = ''γ'' in the complex plane such that ''γ'' is greater than the real part of all singularities of ''F''(''s''). This ensures that the contour path is in the region of convergence. If all singularities are in the left half-plane, or ''F''(''s'') is a smooth function on −∞ < Re(''s'') < ∞ (i.e., no singularities), then ''γ'' can be set to zero and the above inverse integral formula above becomes identical to the inverse Fourier transform. In practice, computing the complex integral can be done by using the Cauchy residue theorem. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Inverse Laplace transform」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.