Volume Elements (dV) in Cartesian, Spherical, and Cylindrical Coordinates

Just a video clip to help folks visualize the primitive volume elements in spherical (dV = r^2 sin THETA dr dTHETA dPHI) and cylindrical coordinates (dV = r dr dPHI dz). In spherical coordinates, the lengths of the edges of the primitive volume chunk are as follows: one side is "dr," another side is "r dTHETA," and another is "r sin THETA dPHI." When people are first learning this stuff, they often have a hard time seeing that the little length that is being swept over dPHI is r sin THETA. Here, I've used the physics/engineering and non- American mathematician convention that the angle THETA comes from the z-axis or "north pole." American mathematicians tend to reverse the meaning of THETA and PHI, such that phi comes from the north pole. For them, dV is r^2 sin PHI dr dPHI dTHETA. Whatever. Call the coordinates Jim, Bob, and Sue if you'd like. Note: if the system you are working on has no angular dependence, use dV = 4 pi r^2 dr dTHETA dPHI in spherical coordinates. #calculus #multivariablecalculus #math

[pleurote]

I can't even explain how long I have searched for this video. You are a life saver!

[namangoyal]

Such a nice explanation, I was looking for the conversion b/w various systems and this video was perfect for clearing my doubts regarding elemental analysis in different coordinate systems. Thank You!!

[gokcecesmeli]

This video is incredibly helpful, thank you so much!