Short for the divergence of a quantity. In an orthogonal coordinate system with coordinates {u_{1},u_{2},u_{3}}, where a line element *ds* is given by

ds²=h_{1}² du_{1}² + h_{2}² du_{2}² + h_{3}² du_{3}²

then the divergence of a

vector quantity

**A**; is given by

div **A** = (1/h_{1} h_{2} h_{3})(δ/δu_{1} {h_{2} h_{3} **A**_{1}} **i**_{1} + δ/δu_{2} {h_{3} h_{1} ** A**_{2}} **i**_{2} + δ/δu_{3} {h_{1} h_{2} **A**_{3}} **i**_{3})

where

**i** is the

unit vector
In cylindrical coordinates

{u_{1},u_{2},u_{3}} = {R,φ,Z}

{h_{1},h_{2},h_{3}} = {1,R,1}

'Div' is usually represented by a triangle 'pointing' downwards followed by a full stop (to distinguish it from grad)

'div' is often used in electromagnetic theory. Together with its cousin the operator 'curl' it allows an elegant expresion of Maxwell's equations. For example the the empirical obervation that there are no magnetic monopoles is expressed in one of those venerable equations as

div.B = 0

See also grad.