HI, Dr.Clark im just confused with the value that we get after computing the triple integral. In the 1st example, we get 3/2, so what does this actually means? It is a scalar right? I've read online where a positive number means positive divergence where larger arrow implies greater magnitude, but here we are required to calculate the surface? So does the value 3/2 has a value like m^2 or something? Im new to this div, curl thing as i am about to enter my Analysis 2 class.
The valued 3/2 is a scaler. It's a measure of the "flux" out the surface of the vector field. So, if the surface is a net, and the vector field is the flow of water, the flux would be how much water is flowing through the net. So the units depend on the units of the vector field - it's could be an electromagnetic field and then you'd have to ask a physicist what the units mean in that case. If you're looking for a nice book that explains divergence and curl in a conceptual way I'd suggest "Div, Grad, Curl, and All That". It's a friendly and short read.
in cylindrical coordinates, you need to have dV the volume differential, which is r dz dr dtheta. In rectangular coordinates, it is just dV = dx dy dz, a box, but in polar coordinates dx dy = r dr dtheta, so in cylindrical, dV = r dz dr dtheta. You'll need to look at a picture of the polar "rectangle" r dr dtheta from a textbook to see why the r is there.
This is what i needed !!
Glad it was helpful!
HI, Dr.Clark im just confused with the value that we get after computing the triple integral. In the 1st example, we get 3/2, so what does this actually means? It is a scalar right?
I've read online where a positive number means positive divergence where larger arrow implies greater magnitude, but here we are required to calculate the surface? So does the value 3/2 has a value like m^2 or something? Im new to this div, curl thing as i am about to enter my Analysis 2 class.
The valued 3/2 is a scaler. It's a measure of the "flux" out the surface of the vector field. So, if the surface is a net, and the vector field is the flow of water, the flux would be how much water is flowing through the net. So the units depend on the units of the vector field - it's could be an electromagnetic field and then you'd have to ask a physicist what the units mean in that case.
If you're looking for a nice book that explains divergence and curl in a conceptual way I'd suggest "Div, Grad, Curl, and All That". It's a friendly and short read.
So good thank you!!
Thanks for watching Alexis. Glad it was helpful.
hay quá ♥
fascinating
Why did you write the additional 'r' at 6:31 ?
in cylindrical coordinates, you need to have dV the volume differential, which is r dz dr dtheta. In rectangular coordinates, it is just dV = dx dy dz, a box, but in polar coordinates dx dy = r dr dtheta, so in cylindrical, dV = r dz dr dtheta. You'll need to look at a picture of the polar "rectangle" r dr dtheta from a textbook to see why the r is there.
you're fucking life saver
@@dr.clarkteachesmath i've got question so if dx,dy,dz = r, dr, dz, because dx, dy = r dr so
why do you add "dθ" with the r dr dz dθ 6:42
6:31
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