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# 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: $\nabla \times \mathbf{F}$