Complex Variables Math: Example of a Harmonic Function

Some of my students requested an extra example to show how to obtain the analytic function f(z) from its Harmonic Function.

Basically, if a function f(z) is an analytic function, it must satisfy Cauchy-Rimann equations. Also, then it real part is called a harmonic function and its imaginary part is called a harmonic conjugate function. Each of the harmonic functions must satisfy Laplace's equation.

This concept is useful in electromagnetic problems, where the radiating function is called a Harmonic function, but we would like to use its analytic version, so that the solution to the partial Diff. equations becomes much easier.

[muhammadabdulrahim]

The differentiation for respect to y is wrong