Calculus 3: Divergence and Curl (3 of 26) What is the Divergence?

In this video I will explain what is the divergence, del operator F(vector)

[chrisb]

Great explanation! The divergence is very useful in fluid mechanics. Following with what professor Biezen stated, if we consider a small volume of fluid then the divergence of the velocity equal to zero of the fluid moving through the small volume describes the conservation of mass law ! Think about it if the divergence of the velocity is zero then mass is conserved for an incompressible fluid since the same amount of fluid that enters the volume must also leave it. IF more fluid left the volume than entered it this would mean the divergence is not zero and mass is being created within the volume and is not physically possible for an incompressible flow (liquid flow). Hence in fluid mechanics the divergence of the velocity is always equal to zero for an incompressible fluid and this is the continuity equation of the famed Navier-Stokes equations!

[littlemutt]

lol when he said about the bank account i was like WHUTTT LMAO

[mavmassey]

You are most definitely brilliant sir. My Professors could only wish to be half of your caliber. I was so lost on these concepts, but now I feel confident for my upcoming exams. You are invaluable to all those trying to learn. Thank you for your service.

[juliuswanyama]

You make learning vector calculus a fun experience.

[Yoooomanwhatsup]

In my country teachers only teach us how to do do maths in vector but never tells what it really is . Thanks to you sir . It much more clear to me now. Old is always gold.

[altuber_athlete]

Note: drawing a box is a great way to visualize the divergence of a vector field *at that region* of the vector field in the _plane._ However, the divergence is actually when we _make that box smaller and smaller, _ in other words, we make it an infinitesimal area. In the case of a vector field in the 3D space, then our box will be 3D too, and then the divergence will be the infinitesimal *volume.*

EDIT: never mind, I just realized you said that later in the video xD

[Teturarsyra]

The box explanation is by far the best I've come upon :)

[ruhamasidqy]

very cler explanatian, thank you very much

[marcoventura]

Good video. I can't grasp the intuition behind the fact that even if the functions M, N and P have x, y, z as arguments, when it comes to the formula for divegence we consider only the partial of M wrt x, the partial of N wrt y and te partial of P wrt z. I imagine that for a robust explanations we need real analysis but some "intuition" would be useful.

[surojdey]

Sir, then how is divergence different from a flux? ( A net change of flux?)

[nathancleavinger]

Thanks for the videos! They are very helpful

[taladiv]

The box explanation gave me a clue. Thank you sir.

[abdulrahmanmohamed]

why is the playlist for fiv and curl only until 37 out of 50? wheres the other vid?

[mahendrapanda]

Please make video on gradient, divergence, curl and laplacian operator in orthogonal curvilinear coordinate

[SidharthShambu]

video number 4 is missing in this play list! !!!

[soureachsak]

Excuse me, I dont really know what is victor fields. Can you briefly explain it? And do you have videos for it? Thank!

[jenniferchristinebragg]

Here I am again now in graduate school looking back at your videos for reference. I don't know if you remember me but I popped into your lecture maybe 2 years ago over the summer at el camino when you were teaching a physics class and I told you I watch your lectures all the time and I live in Hawaii? My friend was in your class at the time. Where is your book you told me you were writing?! I think it was about global warming!? :)

[ajilbabu]

Sir, for positive charge what kind of divergence it can have??

[RedVRCC]

I searched for "3OF26" as in the 3OF26 high explosive fin stabilized 125mm round used by Russian main battle tanks and somehow got here.

[bashirchauhan]

Divergence formula in 'thumbnail' is incorrect.