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# Del

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

In differential geometry, the nabla symbol is also used to refer to a connection.