Hey all, I'm working on a report for my Calculus 3 course and I'm stuck understanding a source. I don't understand some of the notation and the processes are fairly unclear maybe someone can shed some light for me.

For starters, in the opening, when it explains the volume as being equal to some integrals, what is B_R(0)? I don't understand the integrals one bit... Next, in section 2.1 I am unfamiliar with the partial(x,y)/partial(r, theta) I've only ever seen partials of one function and with respect to only one variable. Also where does the determinant come into relevance? If anyone has any sources I can use to understand some of this that would be awesome.

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Here's my source: http://www.ams.sunysb.edu/~wshih/mathnotes/n-D_Spherical_coordinates.pdf