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 <math>\nabla<math>. 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:

<math>\begin{pmatrix}

{\partial / \partial x} \\ {\partial / \partial y} \\ {\partial / \partial z} \end{pmatrix}<math>

The symbol <math>\nabla <math> was introduced by William Rowan Hamilton.

The operator can be applied to scalar fields (<math> \phi<math>) or vector fields (<math>\mathbf{F}<math>), to give:

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

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

See also

• Table of mathematical symbols
• Maxwell's equations
• Nabla in cylindrical and spherical coordinates

Further reading

• Div, Grad, Curl, and All That, H. M. Schey, ISBN 0–393–96997–5
• Jeff Miller, Earliest Uses of Symbols of Calculus (Aug. 30, 2004).
• Cleve Moler, ed., "History of Nabla", NA Digest 98 (Jan. 26, 1998).