What are Harmonic functions? Show that the following function is harmonic and
determine its conjugate function. Also determine its analytic function
f (z) =u+ iv
. Given
that
u= 2x(1-y)
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In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U → R, where U is an open subset of Rⁿ, that satisfies
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xx(x,y)+H yy(x,y) = 0. Harmonic functions arise frequently in applications, such as in the study of heat distributions and electrostatic potentials. Theorem 16.1. If f is analytic in a domain D and f(x+iy) = u(x,y)+iv(x,y), then u and v are harmonic in D. Proof
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