Harmonic Function A function f is called harmonic when
Prove that if f is harmonic, then
where C is a smooth closed curve in the plane.
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Laplace's Equation Let and let
(a) Show that .
(b) Show that .
(c) Show that .
(d) The Laplacian is the differential operator
and Laplace’s equation is
Any function that satisfies this equation is called harmonic. Show that the function is harmonic.