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Green’s Second Identity Prove Green’s Second Identity for
Chapter 14, Problem 51AE(choose chapter or problem)
Green's Second Identity Prove Green's Second Identity for scalar-valued functions u and v defined on a region D:
\(\iiint_{D}\left(u \nabla^{2} v-v \nabla^{2} u\right) d V=\iint_{S}(u \nabla v-v \nabla u) \cdot \mathbf{n} d S\)
(Hint: Reverse the roles of II and v in Green's First Identity.)
Text Transcription:
iiint_D (u nabla^2 v - v nabla^2 u)dV = iint_S (u nabla v - v nabla u) cdot n dS
Questions & Answers
QUESTION:
Green's Second Identity Prove Green's Second Identity for scalar-valued functions u and v defined on a region D:
\(\iiint_{D}\left(u \nabla^{2} v-v \nabla^{2} u\right) d V=\iint_{S}(u \nabla v-v \nabla u) \cdot \mathbf{n} d S\)
(Hint: Reverse the roles of II and v in Green's First Identity.)
Text Transcription:
iiint_D (u nabla^2 v - v nabla^2 u)dV = iint_S (u nabla v - v nabla u) cdot n dS
ANSWER:Solution 51AE
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