Encyclopedia > Del

  Article Content


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:

Further reading

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
Communes of the Aube département

... Bois[?] - Engente[?] - Épagne[?] - Épothémont[?] - Ervy le Châtel[?] - Essoyes[?] - Estissac[?] - Étourvy[?] - Étrelles sur Aube[?] Faux Villecerf[?] - Fay lès ...