翻訳と辞書
Words near each other
・ Time in India
・ Time in Indiana
・ Time in Indonesia
・ Time in Iraq
・ Time in Ireland
・ Time in Jordan
・ Time in Kansas
・ Time in Kazakhstan
・ Time in Kentucky
・ Time in Kenya
・ Time End
・ Time Enough
・ Time Enough at Last
・ Time Enough for Love
・ Time evolution
Time evolution of integrals
・ Time Expired
・ Time Expired (1992 film)
・ Time Expired (2011 film)
・ Time exposure
・ Time Exposure (Little River Band album)
・ Time Exposure (Stanley Clarke album)
・ Time Express
・ Time Fades Away
・ Time Festival
・ Time Flies
・ Time Flies (band)
・ Time Flies (Billy Ray Cyrus album)
・ Time Flies (film)
・ Time Flies (John Michael Montgomery album)


Dictionary Lists
翻訳と辞書 辞書検索 [ 開発暫定版 ]
スポンサード リンク

Time evolution of integrals : ウィキペディア英語版
Time evolution of integrals

In many applications, one needs to calculate the rate of change of a volume or surface integral whose domain of integration, as well as the integrand, are functions of a particular parameter. In physical applications, that parameter is frequently time ''t''.
==Introduction==
The rate of change of one-dimensional integrals with sufficiently smooth integrands, is governed by this extension of the fundamental theorem of calculus:
:\frac\int_^f\left( t,x\right) dx= \int_^\fracdx+f\left( t,b\left( t\right) \right) b^\left( t\right) -f\left( t,a\left( t\right) \right) a^\left( t\right)
The calculus of moving surfaces〔Grinfeld, P. (2010). "Hamiltonian Dynamic Equations for Fluid Films". Studies in Applied Mathematics. . ISSN 00222526.〕 provides analogous formulas for volume integrals over Euclidean domains, and surface integrals over differential geometry of surfaces, curved surfaces, including integrals over curved surfaces with moving contour boundaries.

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「Time evolution of integrals」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.