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
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