Short for the divergence of a quantity. In an orthogonal coordinate system with coordinates {u1,u2,u3}, where a line element ds is given by
ds²=h1² du1² + h2² du2² + h3² du3²
then the divergence of a
vector quantity
A; is given by
div A = (1/h1 h2 h3)(δ/δu1 {h2 h3 A1} i1 + δ/δu2 {h3 h1 A2} i2 + δ/δu3 {h1 h2 A3} i3)
where
i is the
unit vector
In cylindrical coordinates
{u1,u2,u3} = {R,φ,Z}
{h1,h2,h3} = {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.