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m RTT is only used for time derivatives, so the article is changed to reflect this. |
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In [[differential calculus]], the '''Reynolds transport theorem''' (also known as the Leibniz–Reynolds transport theorem), or in short '''Reynolds theorem''', is a three-dimensional generalization of the [[Leibniz integral rule]] which is also known as [[differentiation under the integral sign]].
The theorem is named after [[Osborne Reynolds]] (1842–1912). It is used to recast time derivatives of integrated quantities and is useful in formulating the basic equations of [[continuum mechanics]].
Consider integrating {{math|'''f''' {{=}} '''f'''('''x''',''t'')}} over the time-dependent region {{math|Ω(''t'')}} that has boundary {{math|∂Ω(''t'')}}, then taking the derivative with respect to time:
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