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Spherical vs cylindrical notation

  • Thread starter Calpalned
  • Start date
  • #1
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Homework Statement


Plotting a point in spherical coordinates means using the format ##(\rho, \theta, \phi)## in place of ##(x, y, z)##. Taking a triple integral means replacing ##dV## with ##\rho ^2 sin(\phi) d\rho d\theta d\phi ## As you can see, ##\rho, \theta, \phi ## are all in the same order.

However, for cylindrical coordinates, my textbook plots ##(r, \theta, z)## for points, but replaces ##dV## with ##r dz dr d\theta ##. Why are the three integrals suddenly switched around?


Homework Equations


n/a

The Attempt at a Solution


Is there a reason behind this? I dislike rote memorization
 

Answers and Replies

  • #2
blue_leaf77
Science Advisor
Homework Helper
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Nothing to worry about, ##dV## is an elemental volume with the shape of a "box". You won't care how you are going to arrange the order of the formula for the volume of a box, will you.
 
Last edited:
  • #3
33,632
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I mostly agree with blue_leaf77 -- the order of integration doesn't really matter. The "box" is a rectangular paralellipiped in cartesian coordinates, but in cylindrical or spherical coordinates, the ends aren't flat, and the "box" tapers toward the small end.
 

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