Del

In vector calculus, del is a vector differential operator represented by the symbol <math>\nabla</math>. The name of this symbol is the nabla, after a Hebrew stringed instrument with a similar shape, and so the operator is also called the nabla operator.

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, and is sometimes called nabla, after the ancient Hebrew instrument which the shape resembles.

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>

See also:

• Laplace operator
• Table of mathematical symbols
• Maxwell's Equations

Further reading

• Div, Grad, Curl, and All That, H. M. Schey, ISBN 0-393-96997-5