Uploaded December 2017 | Updated September 2026, 2 weeks ago
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!
Prerequisites: The first two videos of this playlist: youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD and this video on Green's Functions for ODEs are essential: youtube.com/watch?v=Jws70qd-XRw - the rest of the videos in the PDE playlist are helpful but optional.
Lecture Notes: drive.google.com/open?id=1uP8WlVed4T6zVcm8y-3WwSQn2GPY_7nz
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons:
- Jennifer Helfman
- Justin Hill
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
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!
Prerequisites: The first two videos of this playlist: youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD and this video on Green's Functions for ODEs are essential: youtube.com/watch?v=Jws70qd-XRw - the rest of the videos in the PDE playlist are helpful but optional.
Lecture Notes: drive.google.com/open?id=1uP8WlVed4T6zVcm8y-3WwSQn2GPY_7nz
Patreon: patreon.com/user?u=4354534
Twitter: twitter.com/FacultyOfKhan
Special thanks to my Patrons:
- Jennifer Helfman
- Justin Hill
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
