# The Laplacian and harmonic functions The quantity V-Vu-V2u, called the Laplacian of the function u, is particularly useful in applications. (a) For a function u(x, y, z), compute V Vu (c) A scalar va... The Laplacian and harmonic functions The quantity V-Vu-V2u, called the Laplacian of the function u, is particularly useful in applications. (a) For a function u(x, y, z), compute V Vu (c) A scalar valued function u is harmonic on a region D if V a all points of D. Compare this to Laplace's equation eu +Pn=0 and ψ" + ψ”=0. ##### Add Answer of: The Laplacian and harmonic functions The quantity V-Vu-V2u, called the Laplacian of the function u, is particularly useful in applications. (a) For a function u(x, y, z), compute V Vu (c) A scalar va...
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