Question: The Laplace operator is defined by = xx + yy . A function u(x, y) satisfying the Laplace equation u =

The Laplace operator Δ is defined by Δƒ = ƒxx + ƒyy. A function u(x, y) satisfying the Laplace equation Δu = 0 is called harmonic.

Show that the following functions are harmonic: (a) u(x, y) = X (c) u(x, y) = tan- Y X (b)u(x, y) = e cosy

Show that the following functions are harmonic: (a) u(x, y) = X (c) u(x, y) = tan- Y X (b) U(x, y) = e cosy (d) u(x, y) = In(x + y)

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