Del - Definition


Del - Definition

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

Further reading