Spherical Coordinates Derivation

In this video, I derive the equations for spherical coordinates, which is a useful coordinate system to evaluate triple integrals. Then, I show that the Jacobian when using spherical coordinates is rho^2 sin(phi). Enjoy!

[@kartavyagaur7263]

Thank you so much!! No videos, or my teacher could've explained this as well as you!!.

[@EssentialsOfMath]

Why do mathematicians and physicists swap theta and phi?

[@fluffymassacre2918]

They also switch the x,y and z axis,

[@XanderGouws]

Because physicists are dumb

[@aram9167]

@@XanderGouws Ironically spherical coordinates are more useful in physics than math.

[@hassanalihusseini1717]

@@XanderGouws But we have biscuits....

[@marcioamaral7511]

@@aram9167 Not really

[@fulonghuang3771]

Theta is a circle with a HORIZONTAL line across it, it's Horizontal. Phi has VERTICLE line across the circle, so it's Verticle

[@drpeyam]

WOOOOOOW, I’m gonna use that in my class now!!! 😱

[@joehoman3117]

Except physics uses the opposite convention

[@rileystewart9165]

Thank you Dr. Peyam, I miss multi-variate calc. I like to go back to old class stuff to make sure I'm keeping it fresh in my head.

[@izzygrandic]

You are an amazing teacher.

[@ssdd9911]

who even decided to use rho instead of r for the radius anyway?

[@drpeyam]

Stewart 🤮

[@satviksrinivas8764]

I think rho was chosen so it isn't confused with r in cylindrical coordinates

[@Rundas69420]

Now we know that every sphere has radius of 2,7something.
Because this "rho" looks very similar to "e".

[@johnchristian5027]

Multivariable calculus is the best calculus :D

[@vladanikin696]

That was one really nice video, Dr. Peyam, and I enjoyed it a lot, but the whole time while I was watching it I just was thinking about that very strange looking "ro". Ρ, ρ - this is "ro". Most of the time it's just P with a little tail. Maybe someone will think about that just like some kind of a nitpicking, but I truly want that a great math teacher, like you, just don't do this kind of "mistakes". Or maybe it's just in my part of the world we write it in this kind of manner

[@vladanikin696]

@@kyro1197 thanks, how I sad, maybe it's just not used in my part of the world. Good to know that ϱ - is ro too.

[@TheNickinator96]

I just finished an electricity and magnetism class this semester, and as a math major I found it difficult at times to go from rho,theta, phi to r, phi, theta. It's pretty annoying.

[@hassanalihusseini1717]

Nice video! Is there a general rule how to get "Spherical" Coordinates in n dimensions?

[@alberteinstein7571]

Nice!!! ^^

[@SuperExodus13]

That's not a rho, it's an e