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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Initial value theorem ： ウィキペディア英語版 Initial value theorem In mathematical analysis, the initial value theorem is a theorem used to relate frequency domain expressions to the time domain behavior as time approaches zero.〔http://fourier.eng.hmc.edu/e102/lectures/Laplace_Transform/node17.html〕 It is also known under the abbreviation IVT. Let : $F(s)\; =\; \backslash int\_0^\backslash infty\; f(t)\; e^\backslash ,dt$ be the (one-sided) Laplace transform of ''ƒ''(''t''). The initial value theorem then says〔Robert H. Cannon, ''Dynamics of Physical Systems'', Courier Dover Publications, 2003, page 567.〕 : $\backslash lim\_f(t)=\backslash lim\_.\; \backslash ,$ == Proof == Based on the definition of Laplace transform of derivative we have: :$sF(s)=f(0^-)+\backslash int\_^e^f^(t)dt$ thus: :$\backslash lim\_\; sF(s)=\backslash lim\_\; ()$ But $\backslash lim\_e^$ is indeterminate between t=0− to t=0+; to avoid this, the integration can be performed in two intervals: :$\backslash lim\_\; ()$ =\lim_\^e^f^(t)dt" TITLE="\int_^e^f^(t)dt">) + \lim_()\} In the first expression where 0−+, e−st=1. In the second expression, the order of integration and limit-taking can be changed. Also $\backslash lim\_e^(t)$ where 0+:$\backslash begin$ \lim_ () &=\lim_\^f^(t)dt" TITLE="\int_^f^(t)dt">)\} + \lim_\\lim_()\}\\ &=f(t)|_^ + 0\\ &= f(0^+)-f(0^-)+0\\ \end By substitution of this result in the main equation we get: :$\backslash lim\_\; sF(s)=f(0^-)+f(0^+)-f(0^-)=f(0^+)$ 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「Initial value theorem」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.