Volume in Spherical Coordinates

craigory

1. The problem statement, all variables and given/known data

express a volume element dV= dx*dy*dz in spherical cooridnates.

lanedance

have a crack mate! any ideas?

craigory

Is it simply to convert x y and z into corresponding spherical coordinates (ie r cos θ etc)

HallsofIvy

One way to do this is geometric- given specific r, [itex]\theta[/itex], and [itex]\phi[/itex], mark off a small "[itex]\Delta r[/itex]", "[itex]\Delta \theta[/itex]", "[itex]\Delta \phi[/itex]" about the point and caculate its volume.

Another is analytic- determine dx, dy, and dz in terms of r, [itex]\theta[/itex], [itex]\phi[/itex], [itex]dr[/itex], [itex]d\theta[/itex], and [itex]d\phi[/itex], then multiply- but remember that multiplcation of differentials is anti-commutative: [itex]a(r,\theta, \phi)drd\theta= -a(r, \theta, \phi)d\theta dr[/itex].