Green's Function

Green's Function
In this video, by popular demand, I will derive Green's function, which is a very useful tool for finding solutions of differential equations.
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[@CornishMiner]

Great derivation Dr Peyam. Did you know that Green was almost entirely self-taught! Just one year of education as a child, and he didn't start his undergrad until he was almost 40.

[@Peter_1986]

I have noticed that Green's Theorem, Stoke's Theorem and Gauss' Theorem show up here and there in pretty much all math and physics courses right after Calculus 3.
It is quite satisfying when new courses use some of the last concepts from a previous course like that - it really gives me the feel that those courses "kick off" from there.

[@matthewkehoe8911]

I think it is \partial\Omega for the boundary condition at 14:14.

[@xavierplatiau4635]

I had never heard of that function !
Thank you !
Can I ask what is the software you used in this video?

[@drpeyam]

Microsoft whiteboard

[@abhijitmahata4149]

Thank you

[@kanthichandra898]

It’s important for M2 in engineering.

[@CaioCostaatsocs]

I loved it! I'm already waiting for the two videos about the Green function in the upper-half plane and in the unit disk!

[@cameronspalding9792]

The Greens function is a way of inverting differential operators

[@VIVI-ev9oc]

I was all down bc I couldn't get this but now I'm all smiley. You make maths a lovely place to navigate ♡

[@Czeckie]

oh man! there's a PDE playlist and I didn't know about it. I'll be in my bunk

[@firemaniac100]

Thanks! Let me suggest you to present the proof of Helmholtz decomposition

[@diegoov926]

Gracias por compartir su conocimiento. Muy gentil.

[@ycciou9718]

I love you. Your perfect explanation rescue my P.D.E. grade.

[@drpeyam]

You’re welcome!!

[@elyepes19]

True, I was waiting for the Green's function video. Thanks Dr Peyman!

[@dominicellis1867]

How do you derive the fundamental theorem for the Laplace equation? I’ve spent weeks trying to solve laplaces equation with non-homogeneous boundary conditions and cannot seem to fix A(x,y)B(y,z)C(x,z).

[@drpeyam]

There’s a video on that!!

[@MarcelloZucchi91]

At 14:12 I think it should be "on ∂Ω" instead of "on Ω"

[@laminebellilet2423]

The photo in the thumbnail is actually of Lord Kelvin. There are no pictures of George Green.

[@drpeyam]

Really? I had no idea haha, it’s the first thing that popped up when I googled green

[@laminebellilet2423]

@@drpeyam There was this article about his life in Physics Today (the Green of Green functions) in which I saw that picture of Lord Kelvin. Apparently, Green wasn't really a professional physicist nor a mathematician (he was a miller !) and so nobody of the community had read his work. It was Lord Kelvin that resdiscovered his essays, years after they had been published, and republished them. An interesting story actually.

[@u.v.s.5583]

@@laminebellilet2423 Indeed, thank you for pointing this out. Green has a very interesting biography.

[@sadface7457]

This is really nice setup.

[@Kdd160]

YOu are the coolest prof I have ever seen keep it up :DDDDD

[@johnm.6975]

I didn’t know I needed this but I did

[@khanster]

Thank Dr. Peyam. I'm on this chapter right meow.

[@shantilalshendage747]

Nice work!!!

[@franciscojavierorozcobeiza9378]

Great video, please the name of your editor

[@ОлександраМаляр-ъ7э]

Thanks!

[@orfeaspapaioannou2755]

sir, which is the video you've done about multidimensional integration by parts;

[@drpeyam]

Check out the playlist

[@jorgericardocamarenacrisan5442]

Books for this? Please. I'm from Perú.

[@drpeyam]

Evans

[@CarlosBrito524]

Just read up on it in Evans !

[@frozenmoon998]

Superb!

[@pinklady7184]

Very interesting, but those is beyond my comprehension, as I am only an intermediate in maths. Someday, I will be back learning this maths. 🙂

[@shandyverdyo7688]

The next is example solving poisson equation using green function please. 💙

[@drpeyam]

How did you guess? 😱

[@shandyverdyo7688]

@@drpeyam Idk. Cz i can read your mind. Hahaha. 🤪

[@ImPresSiveXD]

very nice!

[@bandamkaromi]

Green's function. never seen before. wow.

[@navierstokes2356]

You are using Evan's book for videos regardind PDE's?

[@drpeyam]

Yes

[@douglasstrother6584]

Ch. 8 on Poisson's Equation of
"Modern Electrodynamics" by Andrew Zangwill
www.cambridge.org/core/books/modern-electrodynamics/E5448C70CBF3651B2056F28EBF859AE9
has a detailed presentation on the construction of Green Functions. It's on the level of Jackson without the sharp edges.

[@comedyadda6688]

Sir please make more videos on pde
Green function for half space and unit boll.
Thank you

[@drpeyam]

Check out the playlist

[@comedyadda6688]

@@drpeyam got it sir
Thank you

[@chimetimepaprika]

Next video: Yellow's function

[@ShubhamBhushanCC]

Hallelujah

[@alejandrobarrantes8657]

I would like to learn galois theory, maybe u can help with a nice explanation of it

[@drpeyam]

🤮🤮🤮

[@brianez2643]

epic, subscribed

[@pradyumna8725]

I'm missing the black board🥲

[@SpoonPhysics]

finally

[@sharifabdi3818]

First