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musicmar
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Homework Statement
a. show that delφ=div(gradφ) for any function φ.
b. show that φ is harmonic if and only if div(gradφ)=o.
c. Show that if F is the gradient of a harmonic function, then curl(F)=0 and div(F)=0.
d. Show F=<xz,-yz,1/2(x2-y2)> is the gradient of a harmonic function. What is the flux of F through a closed surface?
The Attempt at a Solution
I did parts (a) and (b), but am now stuck on (c) (and thus (d)). Can someone explain to me what the gradient of a harmonic function is and how you find one? Thanks.