Encyclopedia > Del

Article Content

Del

In vector calculus, del is a vector differential operator represented by the symbol $\nabla$. 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:

$\begin{pmatrix} {\partial / \partial x} \\ {\partial / \partial y} \\ {\partial / \partial z} \end{pmatrix}$

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 ($\phi$) or vector fields ($\mathbf{F}$), to give:

• Gradient: $\nabla \phi$
• Divergence: $\nabla \cdot \mathbf{F}$
• Curl: $\nabla \times \mathbf{F}$

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia
 Search over one million articles, find something about almost anything!

Featured Article
 Sanskrit language ... serves to make the thematic verbs generally more well-behaved. Exponents utilized in verb conjugation include prefixes, suffixes, infixes, and reduplication. Also ...