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Calculus explanation (cartesian ----> spherical coordinates)

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appa
Posts: 2249 - Karma: 1,740
i was in a calc 4 class last year (i was on the quarter system) and we were learning really quickly about double and triple integrals and some vector and multivariable stuff. one thing that my professor skipped over that i don't understand is why you add p^sin(phi)dpdthetadphi when switching from cartesian to spherical coordinates. can anyone explain this to me? does it have something to do with a thing called jacobian?
12 years ago
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DrZoidberg
Posts: 5676 - Karma: 4,299
If I remember correctly, if you do the jacobian transformation, you find that you need to add that to the end of the integral. I believe I did it like a year ago, but I can't remember. I just remembered that that was the take home lesson of that topic. So if you want to prove it to yourself, you'll have to look up how that's done.
12 years ago
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appa
Posts: 2249 - Karma: 1,740
thanks i just didn't know exactly what to look for. i remember a friend of mine was in a different calc class and they spent some time on jacobian and i guess my professor didn't think it was important.

we can let this thread die now.
12 years ago
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LoathesRaisins
Posts: 3612 - Karma: 4,735
Ask Chicken
12 years ago
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chickenonabun
Posts: 461 - Karma: 285
I'm in calc BC (what i think is Calc 2 in college) and this sounds hard. i might have to do it cuz i might minor in math in college...
12 years ago
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appa
Posts: 2249 - Karma: 1,740
yeah you probably will in calc 3
12 years ago
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DrunkRandy
Posts: 189 - Karma: 171
Khanacademy.com
12 years ago
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Rparr
Posts: 5733 - Karma: 48,751
When I learned that material, they told us it's not important WHY it's there, but to know how to use it.

But that's because I'm an engineer and they put us in calc classes focused on application of the stuff, most likely.

It's just there, like how you add r dr d(theta)dz to the integrand when you go into polar/cylindrical coordinates from rectangular.
12 years ago
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yuck
Posts: 8384 - Karma: 2,090
wolfram alpha is the best calculus resource on the internet IMO, and you dont have to sit through all the videos like khan academy.
12 years ago
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