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Del

From Biocrawler, the free encyclopedia.

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:

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

The symbol ∇ was introduced by William Rowan Hamilton.

The operator can be applied to scalar fields ( $φ$ ) or vector fields 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.

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Del

From Biocrawler, the free encyclopedia.

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