Laplace's Equation and Potential Flow

[@anonjo2630]

The fact that this is freely available on youtube is really insanely incredible, I appreciate it so much.

[@JohnSmith-qp4bt]

No it’s not insane. It’s just math. You’re English is tacky. Unpolished.

[@charlesperry7300]

The Professor writes out the subject material on the modern blackboard effectively in sync with clear explanation, making the subject easy to learn. This is what excellent teaching it is.

[@Sulybrainerz]

finding this channel is a treasure for engineering students . thanks professor

[@WilliamDye-willdye]

I look forward to the day when mathematicians mention "flow fields" in a live lecture, and some future variant of Dall-E automatically creates an animated flow field on the screen. Dynamic systems deserve dynamic representation.

[@J2000Ray]

that would be wyyyld

[@Facetime_Curvature]

Just a small issue when it misinterprets things and winds up with NSFW increasing fluid flow through a tightening vortex... you get a very interesting presentation.

[@Mutual_Information]

This channel is so damn good b/c Steve knows so damn much

[@TimothyOBrien6]

Clear and concise. Couldn't ask for more.

[@MM-cz8zt]

Great video! I am extremely impressed that you can write so neatly reversed and backwards. Huzzah! That is a skill in and of itself.

[@rymsharman]

the video is flipped during editing lol

[@돌구름-t8t]

Thank you for this deep theoretic lecture. I agree to your opinion of universal phenomenona. God bless you!!!

[@NicholasRehm]

Steve, what exactly is your background? I can take a guess from the aero/ML content you’ve been pushing out lately, but loving it all nonetheless

[@NITESHKSAHU]

Velocity field can be represented as a gradient of a scalar for irrotational and incompressible flow, even when flow is unsteady and the laplacian of phi =0 is then true for unsteady case where the unsteady peaks in through the unsteady bcs.

[@beebee_0136]

Thank you, Doc.

[@curtpiazza1688]

This is GREAT! I'm learning a lot! New horizons for me! 😊

[@jamesmosher6912]

Love it! Question though, doesn’t the potential field still hold for Div * f x Grad V, where “f” is a scalar function? For example, in the standard wave equation, often derived/thought of as a fixed string under tension, the tension is constant. But, for say, a hanging chain, the tension in the chain varies with height and the governing equation involves something like Div * T(x) x Grad U. Laplace’s equation and the Laplace operator are really just special cases of the former in a homogenous medium. Also, I would LOVE a video about solving Laplace’s equation and the Helmholtz equation (really, finding the Eigenfunctions) on irregular domains. Triangles, or the square with one quadrant removed, etc. Thanks for the video!

[@himanshuraj1482]

Sir, I want to pursue Ph. D. under you. Currently, I am in IIT Bombay, India. I am your big big fan!

[@timothypulliam2177]

An important fact about harmonic functions (functions that satisfy Laplace equation), is that their sum also satisfies Laplace equation. Del^2(f + g) = Del^2(f) + Del^2(g) = 0 + 0 Since the Laplace operator is a linear operator.

[@straightforward4775]

Prof. Steve i am new to all of this, I am becoming your FAN. I am studying fluid mechanics here in france as an international student and you are my beacon of hope. Allah has sent you into my path for that I am greatful.

[@adetunjiquadtature4725]

Nice class.

[@sohailtabarhossain6096]

Thank you sir. It was so helpful

[@arvindp551]

Lgga di lgga di aag lgga di 👏

[@MyGaurav12]

@Eigensteve Great Series, Dr. Brunton. But why the flow has to be steady? Can't the potential exist at all times?

[@kevincardenas6629]

Thanks a lot for these videos! How often are you publishing them?

[@TomatoesPlease]

Hi Steve, is it correct to assume that divergence free means, colloquially speaking, divergence AND convergence free? In other words, it appears that the term divergence accounts both for expanding and retracting systems?

[@Eigensteve]

Yes absolutely, that is a good way to think about it

[@TomatoesPlease]

Excellent. Many, many thanks for sharing this gift with your viewers!

[@daltontinoco7084]

So i have to ask. Steve, are you a wizard at writing backwards or do you just flip the video. I can't tell its bothering me lol. Thank you for all that you share!

[@fabiotiburzi]

I think that he is left-handed and he flip the video in post production

[@anthonymaione8307]

Hey when you state steady flow being the change in velocity being zero, does that also mean the vectors are not changing direction based on the definition. So the vector field changes and each vector maybe be different than another but each individual vector is steady?

[@lioneloddo]

What is counterintuitive with mathematics, is that to be more efficient, variables that we can not intuitively know, have to be used. Here, we intuitively understand what is the velocity, but it's better to use another quantity, the potential, that is very abstract. The same for the complex space. We don't know what it is, but it's easier tu use it rather than the real space.

[@andersongoncalves3387]

Thank you!

[@mariovrpereira]

Thank you

[@mrbenson63]

Hello, i just watched the two last videos. I'd be great to deal with streamline function, i mean the scalar field which gradient is orthogonal to a given potential vector field. This is very useful to visualize streamlines.

[@sitrakaforler8696]

Nice video!

[@michaele4151]

Low pass filter the audio please (Thank you for making this video)

[@alexfwfwfw4830]

How the hell do you write backward and still manage to be readable?

[@pk2712]

For me its pretty much easier to do the curl in 3 dimensions for Cartesian coordinates .

[@xa4233]

Can’t understand the complex part, I probably need to step back and check complex variables.

[@chipfoo5115]

I'm lost at complex potential...

[@fabiotiburzi]

That's why it's called complex

[@johnalley8397]

It's weird (complex analysis) after 2 semesters, I still have a very tenuous grasp.

[@Eigensteve]

I’m planning a little mini series on complex, so hang tight!

[@fabiotiburzi]

@@Eigensteve can't wait to see it!!

[@johnalley8397]

@@Eigensteve Lotsa demos, pictures, movies, mathmatica? The symbols fail to provide intuition.

[@s.mammar6117]

Superbe