Why is dxdy=rdrdθ? (geometry vs Jacobian)

In this Calculus 3 tutorial, you will learn how to convert the dV differential from the Cartesian coordinate (i.e. rectangular coordinate) to the polar coordinate. That is, we will see why dxdy=rdrdθ.
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#calculus #bprpcalculus #apcalculus #tutorial

[denelson]

Here's a θ for your video title, bprp.

[Budgeman]

I wish I would have had you as a high school math teacher way back in the eighties. You explain everything in every video in a very clear and simple manner that makes it very easy to follow

[peterandriszak]

I have never really understood why this is until this video. Thanks!

[Random-pmjz]

From a geometrical point of view how can we safely assume that the dA in rectangular coordinates is equivalent to the dA in the polar coordinates?

[UvSekhon-txnt]

I just completed the 100 derivatives vid. I feel like i can do anything now. lol. thank you so much

[Generalth]

I'm going to be a Learning Assistant for a trigonometry class tomorrow. I'm so excited!!!

[profmariogutierrez]

Anyone have a link to the video he's referring to when he says "that we went over last time" at 1:44?

[DarkTouch]

one thing you neglected to say is that dtheta does not have length units, which is why it must be multiplied by a length unit, in this case R, to get an area.

[conrad]

I get the derivative in this transformation can be expressed as a matrix. Ok.
But why is calculating the determinant the correct thing to do?

[draobrevoh]

Stupid question but can you do the process in reverse? What would the Jacobian look like then

[omarfrikhat]

Thanks but why the little arc is rdθ ?

[rockybruno]

Can you do this for the spherical coordinates version?

[OrdenJust]

We write r dee-r d-theta. That is true enough, but wouldn't it be a little more clear, a little more intuitive, if we wrote instead r dee theta dee r? That is, why break up the r dee-theta product, and make the fact that we have a little (curved) rectangle more obscure?

[jomariraphaellmangahas]

Lezgo, new upload in the upcoming days

[therealist]

OMG IT CLICKED. FINALLY. THANK

Edit: "So we see our girlfriend again" LMAOOO.

[attiladalmadi]

Why is dxdy=rdrd(theta)? (geometry vs Jacobian)

[AmiNirdush]

1/first dA≠ second dA
2/ second dA≠rdrd(theta)
So, the proof is wrong.⚠️

[Mediterranean]

Can you solve this limit
lim (x;y) -> 0 of xy arc sin (x)/x^2 arccos (x)

[Starshine]

You were going really well, but then you thought you were over explaining, which you weren't and it sort of lost me. Given that these videos are available for eternity, you might want to think about how to ensure you are giving all the information a weak reader might need, a way to point at segways in the video.

[dalisabe]

We need a proof, not an intuitive explanation.