# Spherical coordinates!

• July 8th 2006, 04:49 PM
luckyc1423
Help!
Hey, im a college student at the university of oklahoma and couldnt figure out this problem, help would be greatly appreciated!

(A)
Find the linearization of the spherical change of coordinates map:
$
f(p; \phi; \theta) = (p)\cos(\theta)\sin(\phi) ; (p)\sin(\theta)\sin(\phi) ; (p)\cos(\phi)
$

(B)
Find the factor by which the linear map you found in (A) scales volume.
• July 8th 2006, 06:29 PM
JakeD
Quote:

Originally Posted by luckyc1423
Hey, im a college student at the university of oklahoma and couldnt figure out this problem, help would be greatly appreciated!

(A)
Find the linearization of the spherical change of coordinates map:
f(p; phi; theta) = ( (p)cos(theta)sin(phi) ; (p)sin(theta)sin(phi) ; (p)cos(phi) ):
(B)
Find the factor by which the linear map you found in (A) scales volume.

The derivative you need is here.

The factor is the absolute value of the Jacobian $\rho^2 \sin \phi .$