Applications: Harmonic Functions
Definition
Harmonic functions are functions that satisfy the equation
$ \frac{\partial^{2} f}{\partial x_{1}^{2}}+\frac{\partial^{2} f}{\partial x_{2}^{2}}+\cdots+\frac{\partial^{2} f}{\partial x_{n}^{2}}=0 $
or $ \large\Delta f = div(\nabla f) = \nabla\cdot\nabla f = \nabla^{2} f = 0 $.
