Divergence Theorem example: Flux across unit cube // Vector Calculus

[@Sasuke-Uchiha]

bro, you just came in real clutch for my final later today

[@DrTrefor]

hey nice! Hope it went well:)

[@alfredandens7911]

Thank you brother, the whole serie have helped me a lot.

[@nat6429]

This was really helpful and clear, thanks so much!

[@michaelwinder7879]

You are a legend! These videos have carried me through my Calc 3 class

[@utsavdesai3451]

Really Helpful for finals next week!!!

[@ManojKumar-cj7oj]

vocabulary 'flux' and 'circulation' makes the questions more interesting and simple

[@张鑫-e9o]

The handwriting of z is a little bit confusing.

[@softwarephil1709]

Yes. I thought some z were 2 (squared).

[@tiomemo8958]

same here lol@@softwarephil1709

[@TheDeluxeBacon]

Thank you for making these, I have my vector calculus final tomorrow lol

[@DrTrefor]

Good luck!!

[@dantepillon]

Hi this is a great video! But I was wondering when you were talking about the deformation theorem, that is; when divF = 0, any 2 closed boundaries share the same flux. What I cannot seem to get is, if divF = 0, should the total flux for any closed boundary also = 0??

[@DrTrefor]

The total flux over all boundaries have to zero, any specific closed region might not be though

[@dantepillon]

@@DrTrefor @Dr. Trefor Bazett thank you very much for replying sir, but I guess what I still don't get is, can you call any specific closed region its own region. And then apply the divergence theorem on that region alone to say it has 0 flux?

[@firstlegend5105]

​@@dantepillon You are correct that if divF = 0, the total flux for any closed boundary should be 0. In other words, the flux entering the boundary must be equal to the flux leaving the boundary. This is actually a consequence of the divergence theorem: if divF = 0, then the integral of F over any closed surface should be 0. The theorem should read: when divF = 0, any 2 closed boundaries share the same amount of flux and the total flux for any closed boundary is 0.

[@chloemirisch8159]

Did you not take the partial derivatives correctly? I thought the partial derivative in respect to x,y,z would be . very confused as to why you added z to each of them.

[@Brenticus12]

the field equation is (xyz, xyz, xyz) not (xy^2, xy^2, xyz)

[@rodaneblackwood1079]

Thanks!

[@j.o.5957]

Nice, good stuff. Question to self: how do I solve this using standard flux calculations? I frankly don't know, don't think I've been through that. Should look into it later.

[@leondavidpedraza8618]

What happened with the x that comes out of the first integration? I am sorry, I missed it, it was too fast for me to be too slow! thanks.

[@im_KiraL]

How did you get yz+xz+xy from this F

[@CaseyKlein]

Thank you!!

[@ShubhamPatel-gx7pb]

If F= yz i + zx j + xy k and S is the part of the surface of the sphere x^2 + y^2 + z^2 = 1 , which lies in first octant , the the value of double integral F•n ds is Sir why we can't use Divergence theorem in this question?

[@DrTrefor]

Divergence theorem ONLY applies to a closed surface, not part of one.

[@ShubhamPatel-gx7pb]

@@DrTrefor Thank you Sir

[@carultch]

@@ShubhamPatel-gx7pb You can often use the divergence theorem as a shortcut to evaluate the flux over a surface that isn't closed, when symmetry works in your favor. Like if it is easier to find the flux over a closed surface using the divergence theorem, and the open surface in question is just one octant of 8 identical octants, that would form a closed surface if you connected them.

[@aashsyed1277]

What is flux core welding and fabrication near me a lot of

[@carultch]

It's an unrelated meaning of the word flux.

[@swayamkumarpatro776]

Sir, can you please attach a list of problems which are very important in this vector calculus course ?

[@emilykang4354]

Thank you for such a clear statement

[@brianofarrell1977]

F*** me, my final was yesterday... never understood the concept and now i do!

[@DrTrefor]

Haha great timing😂

[@zeeeeeeeeeev6493]

good vid

[@NelsonMbigili-es6pw]

💜

[@ironsideeve2955]

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