Gauss Divergence Theorem. Get the DEEPEST Intuition.

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Күн бұрын

• 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
Books by Alexander Fufaev:
1) Equations of Physics: Solve EVERY Physics Problem
en.fufaev.org/physics-equatio...
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Пікірлер: 255

@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 Жыл бұрын

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

@jobebrian Жыл 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 11 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 11 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 11 ай бұрын

As a city bus driver you really have time to think

@jobebrian 11 ай бұрын

@@pandakso3365 Yep.

@malefetsanekoalane4549 7 ай бұрын

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

@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 Жыл 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

@Haveuseenmyjetpack Жыл бұрын

Please explain gauge theory.

@deusexmachina3091 Жыл 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 Жыл 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

@KsmithBlackstar 11 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 10 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.

@newsgo1876 Ай бұрын

Mathematics is a concise description of what we take for granted.

@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.

@piotr1175 Жыл бұрын

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

@tennisfreak312 4 ай бұрын

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

@marcelb6214 Жыл бұрын

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

@fufaev-alexander Жыл бұрын

thank you!!

@JakubS 11 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 11 ай бұрын

Awesome!! :)

@WenGao-ys9rw 25 күн бұрын

Thank you for your explanation! It's the clearest explanation of the divergence theorem I've ever seen. When reading the calculus textbook, it just tell me the theorem and a mathematical proof, but the connection between the divergence theorem and the green theorem is still ambiguous to me. Your animation helps me understand the connection between them! Thank you very much!

@haroonrasheed3844 2 ай бұрын

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

@joeponsford3503 5 ай бұрын

absolutely amazing explanation to do in 9 minutes is brilliant

@manarlab84 11 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!

@renesperb 8 күн бұрын

This is really how one should explain the divergence theorem . It plays a central role in partial differential equations and has many applications. Well done !

@PatrickDonaldson 2 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.

@manpreetsingh-yh5iu Жыл бұрын

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

@jeffreyhowarth7850 Жыл бұрын

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

@Francinun 3 ай бұрын

So much clearer after this, THANKS

@mayonakao2488 Жыл 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 Жыл бұрын

Glad you liked it!

@user-tt4ie6mv3v 8 ай бұрын

A very explicit and intuitive explanation. Thanks.

@Tamir_Karniely Жыл 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!

@1bite- 6 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

@Britishbaptist Жыл бұрын

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

@rx5514 Жыл бұрын

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

@trippstreehouse 6 ай бұрын

Great explanation.

@vanshmishra7119 8 ай бұрын

Makes sense now! Thanks for the visual intuition.

@ERFARINGyoutube 2 ай бұрын

Perfect explanation for revision

@1008OH 11 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

@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 11 ай бұрын

You are an Electrical Engineer engineer?

@djredrover 11 ай бұрын

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

@sjonnithors1986 7 ай бұрын

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

@sidpandey2762 Жыл бұрын

Amazing, Sir. Thank you. 🙏😊

@Epoch11 11 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 11 ай бұрын

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

@AdelElsayed-qr9dg Ай бұрын

Excellent explanation❤

@SanzAlfredo Жыл 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.

@lufax 11 ай бұрын

Great step by step explanation

@tanmayshrivastava3687 11 ай бұрын

Thanku so much✨

@alexlo7708 Жыл 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.

@Olaf_Schwandt 11 ай бұрын

brilliant explanation

@bishalsarkar73 11 ай бұрын

Very well explained ❤

@marshmelows 11 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!

@meccamiles7816 10 ай бұрын

Really great video. Well done on the visuals.

@muhittinselcukgoksu1327 Жыл бұрын

thank you so much.

@ww4011 Жыл бұрын

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

@danielarisa1610 Жыл бұрын

Great job man!

@Native_love Жыл бұрын

Beautifully explained! Subbed to your awesomeness!

@denniswandera8582 Жыл бұрын

Easy and simple explanation

@maxqi3729 7 ай бұрын

Pretty epic dude, very underrated

@thomaspham2752 11 ай бұрын

great graphical explanations !

@newsgo1876 Ай бұрын

Surface to the volume, is just like what the two end points are to a segment of line.

@mrhoho 11 ай бұрын

thanks for sharing

@blackhole1222 9 ай бұрын

you earned a new subscriber!

@robertdavie1221 Жыл бұрын

Very good explanation.

@Soundsaboutright42 4 ай бұрын

Dude I wish you were my math teacher growing up 😂

@MusicEngineeer 2 жыл бұрын

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

@ThatBigGuyAl Жыл 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!

@dattu7733 Жыл бұрын

Thank you

@frun 11 ай бұрын

Reminiscent of the holographic principle and ADS/CFT

@user-ec7ry8qo8n 5 ай бұрын

Thx

@moticohen6785 Жыл бұрын

Excellent!

@Amansingh-nl4ev 8 ай бұрын

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

@gastonsolaril.237 11 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"

@gauravchandra1585 11 ай бұрын

Lucky are those who have great teachers or mentors

@user-dy1ke1xe1r Жыл бұрын

Man!! your contribution will be remembered.

@fufaev-alexander Жыл бұрын

oh thank you!

@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

@chongwang7768 6 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.

@Schlaousilein67 11 ай бұрын

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

@theQuantumPenguin Жыл 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.

@Zamperla 11 ай бұрын

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

@fufaev-alexander 11 ай бұрын

Thank your for your positive feedback! :)

@mozartjpn137 Жыл бұрын

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

@lukmanhdrjaya Жыл бұрын

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

@fufaev-alexander Жыл бұрын

no problem !

@WildGamez 2 жыл бұрын

Excellent

@y.8901 10 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 ?

@isarojdahal Жыл бұрын

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

@fufaev-alexander Жыл бұрын

Glad it was helpful!

@atakan716 6 ай бұрын

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

@dylandiaas 11 ай бұрын

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

@nako7569 11 ай бұрын

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

@fufaev-alexander 11 ай бұрын

yes

@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!

@roushankhatri3467 Жыл бұрын

Make a video on Stokes Theorem

@sartajshabeer Жыл бұрын

beautiful!

@a.s.l711 11 ай бұрын

If only my prof teaches like this

@fufaev-alexander 11 ай бұрын

oh, thank you mate!

@theblitz1687 7 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.

@afsarshaikh9654 Жыл бұрын

That was amazing!!!!❤

@fufaev-alexander Жыл бұрын

Thank you very much!

@roushankhatri3467 Жыл бұрын

Mindblowing

@fufaev-alexander Жыл бұрын

Thanks, Roushan! 😃

@learning_with_irving4266 Жыл бұрын

Best explanation of calculus and physics

@fufaev-alexander Жыл бұрын

Thank you very much!

@surendrakverma555 11 ай бұрын

Very good lecture Sir. Thanks 👍

@fufaev-alexander 11 ай бұрын

Thanks for liking

@MossadCIA43 2 жыл бұрын

Stokes and greens theorem please

@imadebouftini316 Жыл бұрын

Important clarification !! this transformation originally belongs to Green and Ostrogradski but not to Gauss

@ismagine Жыл бұрын

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

@AashiqueHussain_ 2 жыл бұрын

wow, you are doing great!

@fufaev-alexander 2 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

@emilr.n.jakobsen8295 11 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 10 ай бұрын

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