The Laplace operator $\displaystyle \Delta$ is defined by $\displaystyle \Delta f = f_{xx} + f_{yy}$. A function $\displaystyle u(x,y)$ satisfying the Laplace equation $\displaystyle \Delta u = 0$ is called harmonic.

Show that $\displaystyle u(x,y) = x$ is harmonic.

First thing, though: What does it mean for a function to be harmonic? The explanation they give is confusing to me. Can you show me how to do this so I can understand how to do my other problems related to this?