Partial Differential Equation

A partial differential equation (PDE) is an equation containing a unknown function of two or more variables, and it’s partial derivatives with respect to these variables.

Harmonic Function

TODO: Explain what this actually is, this is just a placeholder to see how the page looks

A function of multiple variables, for example; $x_1$, $x_2$, $x_3$; $u(x_1,x_2,x_3)=u(\vec{x})$ is harmonic, or a solution of the Laplace equation. If it satisfies the following condition:

$$\frac{\partial u}{\partial x_1}+\frac{\partial u}{\partial x_2}+\frac{\partial u}{\partial x_3}=0$$

This can also be written as:

$${\nabla }^{2}u=△u=0$$

Where $△$ is the Laplacian operator and $\nabla$ is the operator named nabla.