Let S be the boundary surface of a region W in R3 and le
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Let S be the boundary surface of a region W in R3 and let Den? denote the directional derivative of ?, where en is the o
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Let S be the boundary surface of a region W in R3 and let Den? denote the directional derivative of ?, where en is the outward unit normal vector. Let be the Laplace operator defined earlier. (a) Use the Divergence Theorem to prove that S Den? dS = W ? dV (b) Show that if ? is a harmonic function (defined in Exercise 37), then S Den? dS = 0
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