A function ? satisfying ? = 0 is called harmonic. (a) Sh
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A function ? satisfying ? = 0 is called harmonic. (a) Show that ? = div(??) for any function ?. (b) Show that ? is harmo
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A function ? satisfying ? = 0 is called harmonic. (a) Show that ? = div(??) for any function ?. (b) Show that ? is harmonic if and only if div(??) = 0. (c) Show that if F is the gradient of a harmonic function, then curl(F ) = 0 and div(F ) = 0. (d) Show that F = xz, ?yz, 1 2 (x2 ? y2) is the gradient of a harmonic function. What is the flux of F through a closed surface?
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