I wish I had such a professor as you, sir, during my vector analysis course. Thank you for the amazing work, now I feel like I can fill in some gaps ;)
@byronwilliams79772 жыл бұрын
Me too, I hate that shitty profs are even allowed to teach. Just let them do research. Excellent profs like Dr. Steve Brunton do far more for STEM in general; Mathematics in particular, than all the pushing of STEM in the media. I majored in Applied Mathematics and Biology, and I noted how many students dropped out of the harder more challenging classes in part due to profs not giving a damn whether the students grasped the material or not. TLDR; great videos, love your stuff please keep doing what you're doing.
@SarvParteekSingh Жыл бұрын
Everything in this video is perfect, except the "thank you" at the end. It was such an amazing lecture, and I found myself saying "What?! No, thank YOU!"
@mzafarullah46702 ай бұрын
What a gem this video is. The explanation combined with awesome presentation makes it easy to understand. Thank you very much!
@Words-.9 ай бұрын
Thank God for this man who knows how to make the complex simple. The textbook fr makes this way more confusing than it has to be.
@chrisguiney2 жыл бұрын
...I have the sense that you've been waiting a long time to use the Get Stoked! pun :D Well, it got me to engage, so take your upvote ;) I just bought a copy of your book the other week, and I'm looking forward to diving into it along with your lectures here. I haven't gotten a chance to watch this video yet, I've been meaning to say thank you for posting every video that you do. I'm a software engineer that really didn't fit in academia, and had learned a good chunk of the prerequisites for all of your material when teaching myself the math needed for physically based rendering. I started to casually branch into machine learning to satiate my curiosity and was surprised how much of the math I'd learned was transferrable. Your videos have really been elucidating, and have helped me deepen my understanding greatly. You're a great educator, and I really thankful that you've decided to share your knowledge so openly. The format works really well for me, and having the visual aids while we're able to see your face really helps me stay engaged. All to say: Thank you, and please keep the content coming!
@Eigensteve2 жыл бұрын
Lol, believe it or not, I just came up with that the day before I released it. Thanks for buying the book -- I hope you enjoy it!!
@massimilianocassol72522 жыл бұрын
Awesome lesson… when I was studying Analysis II all these theorems were so hard to understand, they were taken “as is”, and seemed so mysterious.
@fhz30622 жыл бұрын
Stoke's Theorem (And Green's too) were the kind of theorem I just accepted as a bizarre true of the Universe when I first met them in the undergraduate course. Nowadays I understand them a little bit better. Watching prof. Button's class reminded me I still find both theorems incredible and some how magic, almost a supernatural mathematical property of the universe. The fact integrals of both sides of the equation are equal stills amuses me.
@DJ-yj1vg Жыл бұрын
This guy has a great knack of connecting a lot of seemingly unrelated concepts
@gabscar12 жыл бұрын
Please never stop making videos!
@Eigensteve2 жыл бұрын
Never stop never stopping
@brendansullivan3408Ай бұрын
Your use of the word "signature" is just great. It changed my view.
@mr.schrodinger7 Жыл бұрын
Professors in our college just write the formula without explaining much. Everything is marks oriented.
@neyhmor7 ай бұрын
Lots of that comes from students, though. Many push back when expected to understand principles, unfortunately. Probably heritage of the school system
@Ulas_Aldag2 ай бұрын
@neyhmor yeah you're probably right. A lot of student only want the final formulas and complain about derivations. But at the same time a university professor should always insist on showing how the formular was derived and how it's supposed to be interpreted. For the sake of academia
@trylatdar40124 ай бұрын
I am doing my computer engineering degree and your playlist not only help me understand vectorial derivative, but also make want to make my own vectorial field processing program on my server. Keep going ❤❤
@nathanzechar55992 жыл бұрын
Thank you math bro. This is what I needed in my life. Mostly Green's theorem, I should have paid attention to that a bit more in EM.
@rodbhar65222 жыл бұрын
This series has been great. Steve, is such an effective teacher.
@ganeshramamurthi966312 күн бұрын
What I was paranoid in college 40 years back has become suddenly a favourite after listening to your lectures. Thank you Professor..🎉
@asirzaki95222 жыл бұрын
Great video professor Brunton. Your teaching skills are immaculate
@MALAYAPH24 Жыл бұрын
Awesome, the professor is able to explain complex concepts into simple way.thanks
@rodrigosimoes52262 жыл бұрын
This ability to tour complex ideas into easy ones is awesome ..... and also, this is the best way to learn
@mariogalindoq Жыл бұрын
Steve: you wrote: A=(1/2)*integral(x dy - y dx), and that is true. But it is also true: A = integral(x dy) = -integral(y dx), so basically you are computing the area two times and then dividing by 2. Nice video, congratulations.
@philipcarpenter99822 жыл бұрын
This is easily my new favorite channel. Content is interesting and very well explained. Thanks!
@innfdtfjord33402 жыл бұрын
Thanks. I mean for all of us could be every interesting to hear about fractal derivative and practices using fractal derivative) Thanks.
@WilliamDouglasHenry3 ай бұрын
Beautiful lecture. I am a UW student in mechanical engineering, and this is awesome. However, I was slightly confused where the F = [ -y, x] come from in the example
@gavinholmes49979 ай бұрын
just realized you were writing backwards the whole time... amazing
@dhickey59192 жыл бұрын
Great content. Your lessons are grounded with intuition and context. I usually end up teaching myself the math courses I've taken, because the intuition component is missing. Thank you!
@kedarpaulCogitoErgoSum2 жыл бұрын
I just that lecture on Stokes and Green's theorem yesterday
@diebutter11872 жыл бұрын
Thank you so much! I couldn't have wished for a better explanation!
@trejohnson76772 жыл бұрын
Although the notation gets heavier, I find Stokes Theorem, and differential forms at large much easier to contemplate when I take the initiative to control the limit implicit in the definition of an integral. Hopefully someone groks this and it strengthens their understanding! Stokes Theorem is close to my heart, as is Fourier’s.
@Eigensteve2 жыл бұрын
Thanks for your intuition on this -- always helpful to see things from a variety of perspectives!
@Martin-iw1ll Жыл бұрын
I thought stokes and gasses theorem reduces to the same thing in differential forms
@trejohnson7677 Жыл бұрын
@@Martin-iw1ll yea p much. That's what makes differential forms op.
@user-nw9nh4hd8p Жыл бұрын
Thank you soo much for such an insightful conceptual explanation! Highly appreciated the lecture!
@alaajaleel85832 жыл бұрын
Amazing better than books and papers i hope to be like you in one day.
@virajkadam30172 жыл бұрын
Thanks a lot for this... I used to be apathetic towards calculus in my ug course. This makes it so interesting.
@curtpiazza16886 ай бұрын
Cool stuff! Great explanation! 😂 I'm watching this along with your series on complex variables!
@glennanderson3744 Жыл бұрын
The mental image that Stoke's theorem conjures for me is imagining if one day, all the wind on Earth blew from the west to the east, at least along the equator. That motivates thinking of the surface integral half as a "net" or "average" curl over the surface, and in this example the "net" curl of the northern hemisphere has to sync up with all the wind on the equator blowing in the same direction. This mental image is intuitive for me in understanding the physical consequences and reasoning behind Stokes' theorem (assuming I understand it correctly hehe)
@nicolabombace20042 жыл бұрын
This is a great explanation! I like how just in the way of explaining and demonstrating with the grid on the kidney bean shape, one can draw similarities between Gauss' Divergence Theorem and Green's Theorem just changing operator. It is also a visual representation that does not require mnemonics at all! I have as well a question: Is there a way to compute surface areas in 3d using Stokes Theorem? Which field should we apply?
@Martin-iw1ll Жыл бұрын
Great lecture! I find interesting is that both Stokes theorem and Gauss theorem have their own versions of the green theorem that is one dimension lower than them
@remyassier1758Ай бұрын
Thanks so much great explanations
@nahblue9 ай бұрын
I loved the trick for computing the area!
@KeyuChen-gc9vrАй бұрын
So helpful! Thank you!
@momokhan56402 жыл бұрын
Amazingly described... Thank you
@kalanakavishanka3152 Жыл бұрын
his teaching is just wow💛
@andersongoncalves33872 жыл бұрын
Great series, Dr. Brunton. Thank you!
@EnipherChawanje10 ай бұрын
This is understandable thanks professor
@Eigensteve10 ай бұрын
Glad it helped!
@UKimpress3 ай бұрын
Very well explained
@anomalous47142 жыл бұрын
This series is fantastic. Since you mentioned potential flow for the next video, I would love to hear a bit about the Helmholtz decomposition and how its potentials relate to the flow of vector fields. Polthier and Preuß (2003; Identifying Vector Field Singularities Using a Discrete Hodge Decomposition) suggested a method for identifying singularities in flow fields by finding the local extrema in the Helmholtz decomposition potentials. However, I don't understand why these potentials are more informative than the local extrema in the divergence and curl of the same field?
@Eigensteve2 жыл бұрын
Thanks, and great questions. Hopefully the next couple of videos start to address these.
@anomalous47142 жыл бұрын
I'm very much looking forward to those! Especially the last question is a mystery to me. 🤔
@House198812 жыл бұрын
Never disapointed... amazing explanation, as alwaya
@anonjo26302 жыл бұрын
this is the best content on the internet
@English1108 Жыл бұрын
Old video so I doubt I'll get a response, but I don't understand the justification for 20:39 when the vector field [-y x] is introduced. it feels arbitrary to make the equation work, but I am really interested in this relationship between the rotation of a closed curve and the area it encloses!!
@DavyCDiamondback Жыл бұрын
It's cool to think about how this shows that there is a "balance" between weather in the northern and southern hemispheres
@techmaster60127 ай бұрын
This guy really know how to teach respect❤
@Eigensteve7 ай бұрын
Thanks!
@jx48642 жыл бұрын
just a little complement, if u wonder why outer product can be calculated by determinant, you can check a concept called wedge product.
@beebee_01362 жыл бұрын
Thank you, Doc. B!
@HD1419372 жыл бұрын
I have to say that the way you draw the different curls of the boxes at 13:00 is kind of confusing. The way it's drawn suggests that the vector field changes direction at the cell boundaries. This is of course not the case in a continuous vector field. I had the same issue with the video on Gauss' divergence theorem. I think a better way to make the concept intuitive would be to say that the vector field has a certain direction at the cell boundary, and explain how this would contribute to curl of opposing sign in the two cells.
@Eigensteve2 жыл бұрын
Interesting point... I'll think about how to make a nice visualization of this.
@ahammedafzal77972 жыл бұрын
Yeah I also felt the same...If all the curls calculated have positive direction as shown in the video,then it would all add up and no cancellation takes place...Why I think the cancellation takes place is that positive curl in one cell forces to have negative curl in the adjacent cell...I also felt the same for divergence theorem(I commented there also)
@HD1419372 жыл бұрын
@@ahammedafzal7797 Well, it's good to realise that curl/vorticity is itself a continuous vector field. That means that its component in the direction normal to S can be positive over a finite portion of S. And since the division of S into cells is arbitrary, it is possible that adjacent cells have a positive value of the integral of vorticity over their area. The value of this integral over S is equal to the sum of the integrals over the individual cells. In this sense you are right to say that the terms add up. By applying Stokes' theorem you transform the area integrals over the cells to line integrals over the cell boundaries. The cancellation applies to the line integrals over the interfaces between cells, so that only the line integral over the boundary of S remains. With this in mind, the arrows drawn in the video do not represent the vector field itself, but in some sense the values of the line integrals over each segment of cell boundary.
@sahibhasan70952 жыл бұрын
I am the first viewer of this lecture. Thank you
@SRIMANTASANTRA2 жыл бұрын
Thank you professor Steve
@VinayakPathak-xc6kp5 ай бұрын
Why the vector field is [-y x] for the area calculation of the irregular surface ? Love your lectures ❤
@joycewinn67712 жыл бұрын
Since the equator integral represents the total “swirl” or curl in the northern hemisphere, does Stoke’s theorem mean that the total curl in the northern hemisphere always equals the total curl in the southern hemisphere? … and if a contour is confined to the border of a hurricane, then that integral says the total curl in the storm equals the total curl in the rest of the world?
@cyocs477311 ай бұрын
What happens when The Fluid has curls in different direction because then they add up for example when there ist a positiv curl and left from it one with negative curl. They would add up in the middle and not cancel each other out so that greens or strokes equation are no longer useable.
@laxmanyadav60582 жыл бұрын
very must crystal clear explation
@megistone2 ай бұрын
Nice video and thanks a lot! But I have left with one question. So, we can take any "slice" dS on the 2D surface S on 3D space and then integrate over perimeter? And if yes - can we take the upper "slice" dS_max (so on sphere it will be point) and what going to happen? And if no - how we can choose where to take "slice" dS?
@jacobvandijk65256 ай бұрын
@ 1:49 This is a 3D-vector, not a 2D-vector as stated here.
@spyhunter00663 ай бұрын
Can we just say Stokes theorem is in 3D but Green theorem is in 2D? They are indeed the same equation. In addition, what they really do is to connect the surface to the line integral for us to solve problems.
@arvindp5512 жыл бұрын
Loved the thumbnail😁
@MatthewGale-s2w7 ай бұрын
😊 you said a bean Inner criteria equaling 1 to an outer of 0 Life was considered strange Considering to its Masters hand not the slave of the lip
@user-yl5yf2fk2f9 ай бұрын
Excellent presentation! Can you connect with a mechanical device called a "Planimeter"? It measures area by walking around the perimeter. Still useful even today!
@trevorgdn12 күн бұрын
At 9min, I'm confused how he went from dA which was a vector to dxdy?
@jphitidis2 жыл бұрын
I love this series! Just a question about the graphical intuition for the curls cancelling - it doesn't seem obvious to me that the curls in the neighbouring cells will be equal and hence cancel. I have one idea to answer my own question. These areas are infinitesimal and hence so near to each other that neighbouring curls are the same because they are essentially "in the same place". Is this correct? If not, please would you explain!
@kolimolitornefr4644 Жыл бұрын
i think you can see the arrows canceling each other out. in the middle of the surface its obvious. then the arrows on the upper side of the surface get canceled by the arrows on the lower side of the surface i think.
@christopherpenn4921 Жыл бұрын
Can't you just find the area of a hypocycloid by subtracting off a circle who's radius is the same as half the side length of the related square?
@DerekWoolverton2 жыл бұрын
When I started watching this video I had a small headache. When I finished I had a bigger one. I guess it just seems like your are throwing away a great deal of information about the dynamics of the field by only measuring its impact on the border. When there is a hurricane approaching land, I don't really care how much its impacting the wind down in the equator; I want to know if I'm still going to have a roof on my house. Will hope further examples further explain when these aggregates are more valuable than the details of the field itself.
@emrekt227 ай бұрын
is there any reason as to why the vector field F for computing acres of land is ? thanks
@afrozashirin71712 жыл бұрын
I like your videos a lot. May I know what kind of tools/software do you use to make your video?
@eggxecution Жыл бұрын
amazing
@Eigensteve Жыл бұрын
Thanks!
@phenomenal46909 ай бұрын
I'm studying mechanical engineering, in what course will i learn and use this formulas ?
@saswatachattopadhyay19764 ай бұрын
Magnificent from india
@flaguser41962 жыл бұрын
the planimeter is an old mechanical device that is said to measure area using green's theorem. it seems earth is flat enough for green's theorem to work, haha.
@vasilisbalas44318 ай бұрын
what blows my mind is the fact that he has to mirror everything he writes
@nd4000Ай бұрын
The camera is behind the transparent whiteboard and flips it.
@sriram73274 ай бұрын
Sir I understood about curl of the vector but why is it dotted with da??? Pl tell me
@fabiangn80222 жыл бұрын
Gracias.
@Anand_Agrawal2 жыл бұрын
Thanks Prof. Brunton. May I ask you why are the last two videos not visible?
@DiegoTomohisa2 жыл бұрын
Are you writing backwards? Or is the video flipped once you finished recording?
@someonestolemyname2 жыл бұрын
The video is flipped, he is using a lightboard. Since he is left handed(you can check his older videos), it looks like he is writing normally to us.
@andreacomparini9381 Жыл бұрын
great great
@issamn.e90322 жыл бұрын
Legend ❤️
@xsli2876 Жыл бұрын
I don't get how to find out the area of the irregular shape property by walking around it and counting the # of steps on y axis and x axis. Can anybody help me? Thank you very much.
@protosstassadar20 Жыл бұрын
I have a question. Green theorem is still valid even that the shape has those spikes like in the last example? That does not makes issues due to the nondifferentiability?
@lucaswilton95774 ай бұрын
late on commenting so i doubt you’ll need this but it’s because it’s considered “peace wise” smooth
@mariovrpereira2 жыл бұрын
Awesome
@JamesSteinley Жыл бұрын
how do you make this video? You are opposite to the plane I'm perceiving. Are you writing everything backwards. I wonder if non-calc3 matriculates would even notice this.
@JamesSteinley Жыл бұрын
is there a mirror involve?
@JamesSteinley Жыл бұрын
oh, yeah in your editing software, of course
@geolab61932 жыл бұрын
Is he left handed?
@willpudupakkamАй бұрын
Yes
@adityaali1762 жыл бұрын
Will you also do line/surface integrals?
@pedros86812 жыл бұрын
Am I the only one who thinks the volume is far too low?
@Eigensteve2 жыл бұрын
Sorry about that... trying to fix this in the studio, but keep forgetting to bump it up in post...
@romanowskis1at2 жыл бұрын
damn, i have started thinking about electron flow or magnetic field like wind, that can swirl or curl.
@issamn.e90322 жыл бұрын
Can you do the K.epselon model
@frun2 жыл бұрын
Derivative is the opposite of the boundary 😵😵😵
@innfdtfjord33402 жыл бұрын
Where are you from?
@frun2 жыл бұрын
@@innfdtfjord3340 Russia
@hunnidasiago746 Жыл бұрын
Is he writing from the back or I'm i seeing things
@fdggfgdfgd251 Жыл бұрын
What is the blob?
@zelsu56462 жыл бұрын
Should admit that his hands are magic
@peterwan8165 ай бұрын
im about to get stroke ._.
@drscott12 жыл бұрын
👍🏼
@rayjay137904 ай бұрын
Meh, his lecture ambiance is not my cup of tea… it seems this one is of a series with foundational concepts introduced earlier, for engineering students maybe
@maudentable Жыл бұрын
Awesome 😂
@wushuhsu2 жыл бұрын
You learned Stoke's Theorem in high school?
@gum88882 ай бұрын
are you writing on a glass board?
@gum88882 ай бұрын
It seems to me that lecturer we see is the image of him in the 'mirror'