The laplacion is tex2html_wrap172 .

This is simple in a rectangular basis. It can be found in arbitrary basis by playing with partials. This is pretty messy.

Another method for orthogonal coordinate systems:

Let tex2html_wrap173 and tex2html_wrap174 . Then the coordinates are orthogonal if tex2html_wrap175 satisfy tex2html_wrap176 .

The length element in the new coordinate system is tex2html_wrap177 . So tex2html_wrap178 .

For spherical coordinates,

tex2html_wrap179 . Define tex2html_wrap180 .

For volume integrals, tex2html_wrap181 where tex2html_wrap182 .

For the gradient: tex2html_wrap183 tex2html_wrap184 The inverse matrix is needed so, tex2html_wrap185 so gradient = tex2html_wrap186

For divergence:

source psfile index