math lessons

In Spanish, "del" is a contraction of "de el," meaning "of the," and is often evident in various names.

In vector calculus, del is a vector differential operator represented by the symbol $\nabla$ . This symbol is sometimes called the nabla operator, after the Greek word for a kind of harp with a similar shape (with related words in Aramaic and Hebrew). (Another, less-common name is Atled, because it is a reversed Delta.)

It is a shorthand for the vector:

$\begin{pmatrix} {\partial / \partial x} \\ {\partial / \partial y} \\ {\partial / \partial z} \end{pmatrix}$

The symbol $\nabla$ was introduced by William Rowan Hamilton.

The operator can be applied to scalar fields ( $φ$ ) or vector fields ( $\mathbf{F}$ ), to give:

• Gradient: $\nabla \phi$

• Divergence: $\nabla \cdot \mathbf{F}$

• Curl: $\nabla \times \mathbf{F}$

• Laplacian: $\nabla^2 \phi = \nabla \cdot(\nabla \phi)$