The del operator

The ``del'' operator, also called ``nabla'' operator by some authors, is indicated by an upside-down triangle and is defined by (a triangle over the equality sign means ``by definition''):

$$\boxed{ \nabla \triangleq \hat{x} \frac{\partial}{\partial x} + \hat{y} \frac{\partial}{\partial y} + \hat{z} \frac{\partial}{\partial z} }$$ (2.3)

where $\partial /\partial x$, $\partial/\partial y$ and $\partial /\partial z$ are the partial derivative operators with respect to$x$, $y$, and $z$, respectively.