Gauss Divergence Theorem. Get the DEEPEST Intuition.

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• Gauss Divergence Theor...
00:00 Equation
00:05 Surface integral in the Divergence Theorem
04:21 Volume integral in the Divergence Theorem
07:09 Summary
More: en.fufaev.org/maxwell-equations
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Пікірлер: 250

@fufaev-alexander 2 жыл бұрын

More: en.fufaev.org/advanced-maths Books by Alexander Fufaev: 1) Equations of Physics: Solve EVERY Physics Problem en.fufaev.org/physics-equations-book 2) Alexander Fufaev and His Never Ending Story: en.fufaev.org/lifestory

@bhaviksharma326 2 жыл бұрын

Can you do this for Navier Stokes and RANS turbulence modeling?

@hossamhafez9826 11 ай бұрын

@@bhaviksharma326may it be possible as President of Arab Republic of Egypt has said

@jobebrian 11 ай бұрын

The very essence of clarity. As a city bus driver, I must say this is easily the most straightforward explanation of GDT I have ever heard. Many thanks!

@compegord07 10 ай бұрын

As I read this, all of the connotations of these words arranged this way is almost absurd in what it says: It starts with the hyperbolic “very essence of clarity.” What do you or anyone else generally assume about someone who is a bus driver? If it isn’t that why is it relevant enough to mention? In addition to above, would we assume that any random or even average bus driver would have heard of, knows or thought about GDT?

@jobebrian 10 ай бұрын

@@compegord07 I was just having some fun with some of the other commenters here. Several have said things like, “I’m an Electrical Engineer and this is best explanation …” and “I am a PhD student in Mathematics, and this clearest video …” I really am a bus driver, and although I do enjoy watching videos about math, this was just above my level. I certainly don’t pretend to speak for all bus drivers.

@pandakso3365 10 ай бұрын

As a city bus driver you really have time to think

@jobebrian 10 ай бұрын

@@pandakso3365 Yep.

@malefetsanekoalane4549 5 ай бұрын

You set out to give "the deepest understanding" You achieved this magnicently. Thanks a million.

@KsmithBlackstar 10 ай бұрын

You actually explain things. Most of my professors speak as if I should already know the topic I am learning. You are a savior.

@alphalunamare 9 ай бұрын

Have Faith in yourself! If you do not understand then ASK! Any Prof who looks down at your question is a failed Prof. We all have to learn, it's just that some prof's get so comfortable that they forget their own troublesome journey to tenure. I came from the wrong side of the tracks and did mathematics and upset a few with my up front, no respect, questioning. Luckily there were enough Profs around to shield me from expulsion for being rude in response to a ridiculous answer. What I am saying is that You have the ability to achieve, don't let that be curtailed by a numpty with a superiority complex.

@shobanaa6936 2 жыл бұрын

Sir, I am a physics student, please teach the green theorem and stoke theorem ,I am always support for u,thank u for your teaching,thanks a lot 😊😊

@umbraemilitos Жыл бұрын

They are all versions of the same thing: "The Generalized Stoke's Theorem." If you learn that, you can use those and many other examples.

@savejobar 11 ай бұрын

Pls tell me what course you are in and what university you study at. In Russia, these theorems are studied in the third semester of education

@REASONvsRANDOM 11 ай бұрын

Please explain gauge theory.

@deusexmachina3091 11 ай бұрын

@@savejobar You learn these third semester of your undergraduate or of Doctoral program? I am also a physics student, so I am curious.

@joefuentes2977 11 ай бұрын

@@savejobarIn US it's generally called Calculus 3 or Multivariable calculus or vector calculus. The generalized Stokes' Theorem is usually covered in a course called Differential Geometry

@marcelb6214 11 ай бұрын

I am just amazed. After 6 years of studying this was the best video I have ever seen.

@fufaev-alexander 11 ай бұрын

thank you!!

@piotr1175 11 ай бұрын

That is probably the clearest explanation I've ever had in my life. This is truly brilliant 👏

@petercheng7890 Жыл бұрын

It is so amazing!!!!!!!!!!!. Unlike the book just teaching us how to put the number into it, it explains what exactly we are doing so we can be more easy to understand and accept the concept. Thank you so much.

@JakubS 10 ай бұрын

I was at a taster lecture where a Cambridge professor tried to explain this formula, and I was entirely dumbfounded. But now that I've watched your video, it all makes sense!

@fufaev-alexander 10 ай бұрын

Awesome!! :)

@tennisfreak312 2 ай бұрын

In CFD, Gauss divergence theorem is very important for FVM. Thank you so much for this clear and intuitive explanation.

@dolbodolb6173 8 ай бұрын

Excellent. What prevents the textbook authors to explain things this way with lots of insightful illustrations instead of a wall of formulas!

@joeponsford3503 4 ай бұрын

absolutely amazing explanation to do in 9 minutes is brilliant

@haroonrasheed3844 22 күн бұрын

The best explanation I have seen yet. Thank you bro 🙏

@mayonakao2488 11 ай бұрын

Wish I could like this video twice. I know nothing of the intuition behind Electrodynamics, and yet this made it max’s equations seem as clear as day. Great work!

@fufaev-alexander 11 ай бұрын

Glad you liked it!

@Francinun 2 ай бұрын

So much clearer after this, THANKS

@manpreetsingh-yh5iu 11 ай бұрын

Thanks @Universaldenker for this perhaps most intuitive and meticulous explanation of the divergence theorem.

@manarlab84 9 ай бұрын

This is a gem - I came across it as a suggestion from KZfaq while viewing tutorials about Transformers. The equation in this video gave me a deeper understading of the use of scalar and dot product in understanding the similarties between features and the relationships between features. Thanks a lot!

@tamirkarniely6913 11 ай бұрын

Amazing video! So much explained and illustrated beautifully and detailedlly. A real deep explain for each component in the writing convention. Keep on the exellent work!

@trippstreehouse 5 ай бұрын

Great explanation.

@PatrickDonaldson Ай бұрын

Thank you for posting this, it was a great presentation and helped me review this material to help my nephew who is struggling with it just like I did 30 yrs ago. I now understand this (the math) better than ever! The physical concept has been clear long before tackling the formal math, but it's nice to be able to articulate the concept using the language of math.

@sjonnithors1986 6 ай бұрын

Oh man! I wish I had this video back in 2012 during my first year in Engineering.

@gabrielnegrini8889 2 ай бұрын

Thanks for the great video!!

@ERFARINGyoutube Ай бұрын

Perfect explanation for revision

@jeffreyhowarth7850 11 ай бұрын

This helps me understand more clearly some of Maxwell's equations. I'm also interested in closed forms. Thank you

@AdelElsayed-qr9dg 4 күн бұрын

Excellent explanation❤

@user-tt4ie6mv3v 7 ай бұрын

A very explicit and intuitive explanation. Thanks.

@vanshmishra7119 7 ай бұрын

Makes sense now! Thanks for the visual intuition.

@djredrover Жыл бұрын

I am an EE engineer and I must say, this is THE BEST illustration of GDT I have seen, and I have seen MANY! Well done. (Same with your Maxwell Equation video)

@fredthechamp3475 10 ай бұрын

You are an Electrical Engineer engineer?

@djredrover 10 ай бұрын

@@fredthechamp3475 ahaha I guess I am an EEE! LOL

@Britishbaptist 11 ай бұрын

You have a talent for clarity in your explanation . thank you for this.

@1bite- 4 ай бұрын

the thumbnail does a really good job of relating the divergence integral with the closed loop one i imagine the cubes within the larger cube to represent the infinitesimal points at which you test divergence (it is based off of a derivative after all), and if you just project the surface faces of the infinitesimals to the larger box you get the flux thru the entire surface

@1008OH 10 ай бұрын

Yes I love this intuition as shown on the thumbnail, all of the inner surfaces cancel out and it's just the outermost ones left

@Native_love 11 ай бұрын

Beautifully explained! Subbed to your awesomeness!

@rx5514 11 ай бұрын

It would be better if you could explain more about divergence, but overall this is a highly undervalued channel.

@meccamiles7816 9 ай бұрын

Really great video. Well done on the visuals.

@ThatBigGuyAl 11 ай бұрын

Hi, just to let you know, before the 2:00 mark, you have da_y listed twice in the vectors (you forgot the z component). Great video though!

@Epoch11 10 ай бұрын

It's nice when you have someone who can explain things in a way that are intuitive. Please keep up the good work.

@fufaev-alexander 10 ай бұрын

I will! Thank you very much for your positive feedback!

@sidpandey2762 11 ай бұрын

Amazing, Sir. Thank you. 🙏😊

@lufax 10 ай бұрын

Great step by step explanation

@alexlo7708 11 ай бұрын

If this was to be taught in my undergrad electro magnetic field subject , it'd make us much more understanding than we were then.

@maxqi3729 6 ай бұрын

Pretty epic dude, very underrated

@danielarisa1610 11 ай бұрын

Great job man!

@marshmelows 10 ай бұрын

Very well explained, good speaking rhythm, the visuals were great too, very easy to understand! Loved it I must confess I am revising this information years later I studied this in my college years, so it's easier to understand now. Good luck to my thermodynamics bros and braettes!

@thomaspham2752 9 ай бұрын

great graphical explanations !

@bishalsarkar73 10 ай бұрын

Very well explained ❤

@muhittinselcukgoksu1327 11 ай бұрын

thank you so much.

@Olaf_Schwandt 10 ай бұрын

brilliant explanation

@moticohen6785 11 ай бұрын

Excellent!

@sashamarie3712 Жыл бұрын

Exactly the explanation I was looking for, thank you!

@fufaev-alexander Жыл бұрын

Hey Sasha, thank you very much for the comment!

@robertdavie1221 11 ай бұрын

Very good explanation.

@blackhole1222 8 ай бұрын

you earned a new subscriber!

@Zamperla 10 ай бұрын

This is such a good and visually pleasant explanation! thanks a lot!

@fufaev-alexander 10 ай бұрын

Thank your for your positive feedback! :)

@SanzAlfredo 11 ай бұрын

Sorry... I will use my language to express my opinion about the video.... GRACIAS!!!!! Esto me llevó mucho esfuerzo de entender en mi época de estudiante de ingeniería. La claridad del video es perfecta. Muchas Gracias. Saludos desde La Ciudad del Humo.

@MusicEngineeer 2 жыл бұрын

very well done! thanks you! ...i have the strong hunch that stokes' theorem will be coming soon

@ww4011 11 ай бұрын

Thank you, I just had my exam a week ago, I hope I can know this video before the final ...

@denniswandera8582 Жыл бұрын

Easy and simple explanation

@samisiddiqi5411 Жыл бұрын

Awesome channel. Thanks so much.

@fufaev-alexander Жыл бұрын

Thank you, Sami! #### Want more videos? #### As a channel member you have many cool benefits: ✅ Unlock ALL Physics Videos ✅ Channel Badges For Your Nickname ✅ Unique Channel Emojis ✅ Your Vote Counts 10x in Polls ✅ Immortalization in the Hall of Fame ✅ And that's not all! CLICK -> kzfaq.infojoin

@mrhoho 9 ай бұрын

thanks for sharing

@lukmanhdrjaya 11 ай бұрын

Best explanation i've seen so far. Many thanks for the video dude!

@fufaev-alexander 11 ай бұрын

no problem !

@user-dy1ke1xe1r 11 ай бұрын

Man!! your contribution will be remembered.

@fufaev-alexander 11 ай бұрын

oh thank you!

@a.s.l711 10 ай бұрын

If only my prof teaches like this

@fufaev-alexander 10 ай бұрын

oh, thank you mate!

@dattu7733 11 ай бұрын

Thank you

@frun 10 ай бұрын

Reminiscent of the holographic principle and ADS/CFT

@tanmayshrivastava3687 10 ай бұрын

Thanku so much✨

@Amansingh-nl4ev 6 ай бұрын

Killed it. Now i wonder how flux is a scalar.

@isarojdahal 11 ай бұрын

OMG. THIs is so crystal clear explanation. Thankyou so much .

@fufaev-alexander 11 ай бұрын

Glad it was helpful!

@afsarshaikh9654 11 ай бұрын

That was amazing!!!!❤

@fufaev-alexander 11 ай бұрын

Thank you very much!

@nako7569 9 ай бұрын

basically, what goes out, or comes in, must pass through the surface, am I right?

@fufaev-alexander 9 ай бұрын

yes

@theQuantumPenguin 11 ай бұрын

Error in the graphic of the da vector @1:10 - 1:25 and @1:36 - 1:54, does not matter too much to the presentation which is very well done.

@user-ec7ry8qo8n 4 ай бұрын

Thx

@emilr.n.jakobsen8295 10 ай бұрын

Physicists: “The sum of the forces entering or leaving an imaginary spacial boundary is equivalent in magnitude and direction to the sum of the forces at the boundary itself” College students: “This is getting complicated.”

@alphalunamare 9 ай бұрын

I am not surprised because that is totally incorrect, whom ever said that should be sacked.

@Schlaousilein67 10 ай бұрын

I love it, even if I haven't seen anything yet

@Soundsaboutright42 3 ай бұрын

Dude I wish you were my math teacher growing up 😂

@gastonsolaril.237 10 ай бұрын

This is much easily understood while studying fluid dynamics... "The amount of water that flows through a closed surface, is equal to the change of volume inside the enclosed body"

@atakan716 5 ай бұрын

I wish professors knew how to explain concepts better like this😅 how could one not get this theorem after watching this!🎉

@gauravchandra1585 10 ай бұрын

Lucky are those who have great teachers or mentors

@nicolasfernandes9987 11 ай бұрын

Great vídeo, congradulations 👏

@fufaev-alexander 11 ай бұрын

thanks!

@ismagine 11 ай бұрын

Great video! Btw, there’s a typo on the vector da at 1:41 there are two dy’s missing a dz term

@y.8901 9 ай бұрын

Thank you for your explanation ! Could we say that Green's theorem is exactly analogous to this theorem but with curl instead of divergence ?

@tarikamiri160 11 ай бұрын

Excellent job

@fufaev-alexander 11 ай бұрын

Thank you! Cheers!

@surendrakverma555 10 ай бұрын

Very good lecture Sir. Thanks 👍

@fufaev-alexander 10 ай бұрын

Thanks for liking

@chongwang7768 4 ай бұрын

So it's basically like saying, when you add up everything produced in a country and subtract everything consumed, the result is the exports of the country.

@dylandiaas 9 ай бұрын

I wish I had found this video when I took real analysis II ahaha really good explanation!

@AashiqueHussain_ Жыл бұрын

wow, you are doing great!

@fufaev-alexander Жыл бұрын

Thank you very much! If you like my channel and like my videos, I would be happy about a small donation: tinyurl.com/denker-donate Top supporter appear in the Hall of Fame: universaldenker.org/supporter

@learning_with_irving4266 10 ай бұрын

Best explanation of calculus and physics

@fufaev-alexander 10 ай бұрын

Thank you very much!

@eterty8335 10 ай бұрын

so my guess is that from the perspective of the volume integral, you're splitting the enclosed volume into like infitesimally small cubes, and when you're adding them up, every two adjacent cubes share one face, and both bring it up into the computations but with opposite effects (facing opposite directions), so the inner stuff all gets cancelled out and you end up only with the outer faces, which is just the surface?

@greatgrumble 10 ай бұрын

You don't even need to got that far. The volume integral sums up the sources and sinks that "create" positive and negative flux. Inside that volume. The remaining flux has to flow out of (or into respectively) the volume. Picture each source as a tap and each sink as a drain. If all taps combined carry more water than the capacity of all drains combined, the amount of water increases (And of course the mathematical drain acts as a negative tap so this example also works for a decrease).

@WildGamez 2 жыл бұрын

Excellent

@roushankhatri3467 Жыл бұрын

Make a video on Stokes Theorem

@roushankhatri3467 Жыл бұрын

Mindblowing

@fufaev-alexander Жыл бұрын

Thanks, Roushan! 😃

@sartajshabeer Жыл бұрын

beautiful!

@jeetubais5507 11 ай бұрын

Lovely wow 😍😍😍😍😍superb that's excellence work wow 🤩🤩🤩🤩

@sameedansar3552 10 ай бұрын

Great job❤

@fufaev-alexander 10 ай бұрын

Thank you

@mozartjpn137 11 ай бұрын

The scalar product of two vectors is expressed as the product of a 1x3 matrix and a 3x1 matrix.

@theblitz1687 5 ай бұрын

I have a question. Didnt the tangential F components also came from the cube? But we omitted them through dot product. Why? Since F is a vector field, can it be perpendicular to cube at one side but be diagonal to another side? Your video made the consept a bit clearer so thank you.