In complex analysis, if you take the second derivatives of the Cauchy-Riemmann equations and add them, you get a LaPlace equation that adds to zero in a harmonic function.
In vector analysis, if you add functions that are irrotational (curl=0) and incompressible (div = 0), you also get a Laplacian equation that adds to zero in a harmonic relationship. that is \nabla^2 \varphi = 0 . http://en.wikipedia.org/wiki/Laplace%27s_equation
Are these two applications related in some way? Or is it just coincidental that they both end up on a LaPlacian harmonic function?