Del
In vector calculus, del is a vector differential operator represented by the symbol <math>\nabla<math>. This symbol is sometimes called the nabla, after a Hebrew stringed instrument with a similar shape, and so the operator is also called the nabla operator. Yet another 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 was introduced by William Rowan Hamilton.
<math>\nabla <math>
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:
Further reading
