# Del

For other uses, see Del (disambiguation).

In vector calculus, del is a vector differential operator represented by the symbol ∇. 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:

[itex]\begin{pmatrix}

{\partial / \partial x} \\ {\partial / \partial y} \\ {\partial / \partial z} \end{pmatrix}[itex]

The symbol ∇ was introduced by William Rowan Hamilton.

The operator can be applied to scalar fields ([itex] \phi[itex]) or vector fields F, to give:

 • Gradient: [itex]\nabla \phi[itex] • Divergence: [itex]\nabla \cdot \mathbf{F}[itex] • Curl: [itex]\nabla \times \mathbf{F}[itex] • Laplacian: [itex]\nabla^2 \phi = \nabla \cdot(\nabla \phi) [itex]

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

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