Module 1 : A Crash Course in Vectors
Lecture 2 : Coordinate Systems
  Exercise 5
  The differential element of volume is obtained by constructing a closed volume by extending $r, \theta$ and $\phi$ respectively by $dr, d\theta$ and $d\phi$. The length elements in the direction of $\hat r$ is dr, that along $\hat\theta$$rd\theta$ while that along $\hat\phi$ is $r\sin\theta d\phi$ (see figure). The volume element, therefore, is
 
  Thus the Jacobian of transformation is $r^2\sin\theta$.
 
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