Del Operator

The del operator operates on a scalar to produce a vector. Compare the operation to taking the time derivative. Where δ/δt means to take the derivative with respect to time and introduces a s-1 component to the units of the result, the operation means to take the derivative with respect to distance (in 3 dimensions) and introduces a m-1 component to the units of the result. terms may be called space derivatives and an equation which contains the operator may be called a vector differential equation. In other words A is how fast A changes as you move through space.

In rectangular coordinates

In cylindrical coordinates

In spherical coordinates

See also: Divergence, Laplacian.

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Subjects: Mathematics