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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: : 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.
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