Flux through surfaces | MIT 18.02SC Multivariable Calculus, Fall 2010
ฝัง
- เผยแพร่เมื่อ 2 ม.ค. 2011
- Flux through surfaces
Instructor: Christine Breiner
View the complete course: ocw.mit.edu/18-02SCF10
License: Creative Commons BY-NC-SA
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Why didn't you teach them using the parametrization and taking the cross product of partial derivatives of parametrization to get the normal vector? This dividing by "a" seems to only work sometimes.
Juan Preciado I think this is resuscitation, not a lecture.
@@chriskitley9875 Recitation*
It confused me also
I was use to getting the cross product of the partial derivatives
Thank you for teaching in such a clever way. Keep up the good work. Greetings from Uruguay.
She's fantastic. Thank you.
I love you! Thank you!
Lot of thanks from india👍
Awesome lecture
how did you work out the normals?
did you find out the answer to this, especially for the curved side
You can take gradient of that field and devide magnitude of that gradient
the normal vector is like the parametric equations of ;if you plug that into a graphing calculator using parametric functions you get a full circle, but here we only have from 0-pi/2, which is controlled by the boundary of integration of d-theta. so the professor could have crossed the with the the F = < z ,x , y > and gotten the same. Her (a*d-theta*dz) is her jacobian for her cylindrical coordinates ( r , theta , z). Know t is theta in my example, I'm not writing cos(theta).
@@JG-zn6od amazing. Is that really it?
@@JG-zn6od please teach me, is the gradient of the surface different from taking the partial derivatives Ang getting its cross product?
@MrVandeju Because.. you have to convert to spherical coordinate system.
The formula for converting Rectangular --> Spherical is that z = row cos(phi), and here we know row = a since a is the radius.
Thanku mam for doing your work very well
شكرا😍
Simple and excellent explanation, thanks for share!
the normal calculation explanation confused me so much I stopped watching
hey smartie. your explanation is fantastic, but i wanna ask you something. When the flux is outward, we have to take into account the top and the bottom of the cylinder, but why did you ignore them? Some people may think that they will cancel each other. Actually, this thought is wrong. The bottom will have zero flux, but the top will have some flux.
good explanation
why is there no z in the normal vector
Hi, it means, does not depend of z, n can be anywhere along z
Normal points perpendicular to the surface. There's not really a surface in the x-y plane. So, no z component for normal vector.
You say the normal, but actually you mean the unit normal because you are dividing but 'a'. Am I correct?
Yes
isn't the first one =0, the divergence of F is 0... surface integral is equal to divF of the volume integral
Gauss theorem is invalid for unclosed surfaces
Very clear and objective. Thank you very much
I need a video that this topic is fully explained like teaching a little child. So i can solve even the hardest problem of this topic. But in every video or even my own face to face lectures, teachers don't teach the every aspect of the topic so i am struggling and confusing while trying to solve my textbooks questions.
I Really Like The Video Flux through surfaces From Your
5:45 that zcosϴ should be zacosϴ. you guys should put an annotation as this have been watched 31k times. LUV from INDIA.
No, she did it right... (Remember it's the unit vector, so you have to divide zacosϴ by a, the norm.)
When #MOBI says she wrong. It doesn't matter she is MIT or Oxford, She is damn wrong. No excuse whatsoever will make her right.
ur stupid ... she did it right
MeagaRain84 ok
You're* stupid..
:D:D:D
:D
flux across Surface
∬ F.ñ ds
That's mit
Jumped tons of steps. Bad
This is a class in MIT. And you are from a shit-hole country, so you can't cope up.
You can find this material in any multivariable calculus textbook. It isn't some revolutionary material out of MIT. If your argument is that he cannot understand this material based on his geographical location, then it's only more pitiful that you don't have that excuse and are still here watching the same video because you obviously have trouble with the same concept. Since you yourself have pointed out your issue to be a lack of intelligence seeing that you are from "the proper country" to understand this and still don't...
I do not like the generalized stuff. e.g. using a and h.
asmcriminaL
You should get used to it. They’re just like numbers
Terrible explanation