## Definition of the Laplace Operator

The Laplace operator, represented by $\Delta$, is defined as the divergence of the gradient of a function.

${\large\Delta = \nabla\cdot\nabla = \nabla^{2} = \bigg[\frac{\partial}{\partial x_{1}},\cdots,\frac{\partial}{\partial x_{N}}\bigg]\cdot\bigg[\frac{\partial}{\partial x_{1}},\cdots,\frac{\partial}{\partial x_{N}}\bigg] = \sum\limits_{n=1}^{N}\frac{\partial^{2}}{\partial x^{2}_{n}}}$

## Alumni Liaison

Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett