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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>
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| • Divergence: | <math>\nabla \cdot \mathbf{F}<math>
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| • Curl: | <math>\nabla \times \mathbf{F}<math>
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| • Laplacian:
| <math>\nabla^2 \phi = \nabla \cdot(\nabla \phi) <math>
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In differential geometry, the nabla symbol is also used to refer to a connection.
See also
Further reading
- Div, Grad, Curl, and All That, H. M. Schey, ISBN 0-393-96997-5
- Jeff Miller, Earliest Uses of Symbols of Calculus (http://members.aol.com/jeff570/calculus.html) (Aug. 30, 2004).
- Cleve Moler, ed., "History of Nabla (http://www.netlib.org/na-digest-html/98/v98n03.html#2)", NA Digest 98 (Jan. 26, 1998).
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