a2 f 22 f 2z f = 0 ax2 azz is known as Laplace's equation, after Pierre Simon de Laplace (1749-1827). Any function f of class C2 that satisfies Laplace's equation is called a harmonic function.3 a. Is f (x, y, z) = x2 + y - 2z2 harmonic? What about f (x, y, z) = x2 - y2 + z?? b. We may generalize Laplace's equation to functions of n variables as a2 f 22 f az f + ... + = 0. ax, axn Give an example of a harmonic function of n variables, and verify that your example is correct