Harmonic functions are solutions of Laplace’s equation. We have seen that the real and imaginary parts of a holomorphic function are harmonic. So, there must be a connection between complex functions ...Harmonic functions are solutions of Laplace’s equation. We have seen that the real and imaginary parts of a holomorphic function are harmonic. So, there must be a connection between complex functions and solutions of the two-dimensional Laplace equation. In this section we will describe how conformal mapping can be used to find solutions of Laplace’s equation in two dimensional regions.