Introducing Green's Functions for Partial Differential Equations (PDEs)

In this video, I describe the application of Green's Functions to solving PDE problems, particularly for the Poisson Equation (i.e. A nonhomogeneous Laplace Equation). I begin by deriving the 2 Green Identities, after which I use those identities to come up with an equation for the solution to the Poisson Equation.

Most of the derivations I've done in this video apply to a 3-dimensional case, but as I explain at the end, you could just as easily apply these methods to a 2-D situation as well (in fact, it's slightly easier than with 3-D)!

Questions/requests? Let me know in the comments!

Special thanks to my Patrons:
- Jennifer Helfman
- Justin Hill
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard

[InMattle]

Never stop making these videos, please! I love to see all these topics explained in a better way than they were taught (are being taught) to me at the university :)

[HighlyShifty]

Even though shortly into this video I realised I didnt have close to the prerequisite knowledge to understand this topic, I came away having learnt a lot. I thought youe explanation at 640 was fantastic, thanka

[christopherbriggs]

Dude, These videos are unbelievably good. I'm currently trying to learn/relearn a number of different Mathematics techniques that I haven't looked at in yours or even seen in some cases and your videos are so incredibly helpful. Keep it up!

[riveredge]

I was reading Stanley Farlow's PDE book that covers Green's function very briefly. At some point it shows one equation without proof(p296, notes 1), so I was looking for more info to understand it...and this is it. Thanks! (As a side note, this is an ingenious method to solve this type of PDE.)

[cowgomoo]

Have been struggling with Green’s method for a few weeks now ever since it was introduced in my electromagnetism class. I’ve watched various videos and read the textbooks but really with very little gain in understanding. Thanks a million for this video, I finally feel like I crossed the hump from ignorance into intuition. Especially nice was how simply you derived Green’s identities and then subsequently showed their use in the PDE. Again, I cannot thank you enough. I will go reread my textbooks armed with the lessons I learned from this video.

Do you have any plans on covering the Neumann boundary condition? It’s not strictly necessary since the fundamental concept was phenomenally explained in this video, but more content from you is always welcome.

[snp]

>uses dv as the integrating variable
>uses v, as an arbitrary function

The absolute madlad.

[Legend_Hunter_Original]

Hey Mr khan, I really appreciate these, . You have provided me with good understanding of such topics. I do have a request for you though, can you make a video on solving PDEs (wave equation specifically) using greens function in spherical coordinates ? Like I'm basically trying to solve the main pdes in spherical using greens function. Thanks alot.

[giuseppeguap]

I NEED THE NEXT VIDEO BEFORE FINALS NEXT WEEK PLEASE! :(

[badbreedftw]

Where is the video you talk about at the end? Finding greens functions for different boundaries?

[JoelRTLCosta]

Thanks a lot for the videos!
I would just like to point that a Part 2 video for the 4th Order PDE is missing.

[oyttyoungster]

Excellent video!! Dit you make the follow up video?

[giuseppeguap]

how about some videos on distribution theory? thatd be keeeewl

[kelvin]

Hello! I spent a lot of time on your videos, and they are very helpful!
And I want to ask that do you have any plan to make more videos about this series?

[HelloWorlds__JTS]

(9:43) Not sure I agree with [or understand] your "so it stands to reason" statement; integrate the delta function over either set of variables, and dependence on those variables vanishes. Most of the time I'm left wishing you would give more insights into the meaning behind the steps in your derivations, and tie the derivations into more fundamental concepts (e.g. how the Green's function relates to convolution); but what you offer is so much better than other options, that I shouldn't be complaining. Great videos!

[mavihs]

Did you make the video where you solved PDE's using greens functions ? thanks again for these videos they are very helpful

[arts]

Perfect explanation. You’ve helped me to understand this subject, thank you so much. Already subscribed 👍

[skyishigh]

What's the next part of this video?
I can't find... plz ... Put the link of next video here!!!!

[anilcelik]

Thanks for the effort! Can you make the example video you mentioned please

[zonglehuang]

Very clear and helpful! Thanks a lot!!!

[TheShufflaZ]

This video was super helpful, everything is very well explained in a concise way. The only thing that I'm uncertain about now is how can we apply the boundary condition when the G*du/dn is within an integral?