Solving the 1-D Heat/Diffusion PDE: Nonhomogenous Boundary Conditions

In this video, I solve the diffusion PDE but now it has nonhomogenous but constant boundary conditions. I show that in this situation, it's possible to split the PDE problem up into two sub-problems: one which gives a steady-state solution, and another which gives a transient solution.

I show that the transient solution obeys homogenous boundary conditions, and that using the steady state solution helps to remove the non-homogeneity. Solving the transient solution is just a simple matter of separating variables, in which case these two videos should help:

https://www.youtube.com/watch?v=aq2DAkJIA2w

https://www.youtube.com/watch?v=5AkjTUD6TDw

Questions? Ask in the comments!

Prereqs: My PDE videos so far (see my playlist: https://www.youtube.com/playlist?list=PLdgVBOaXkb9Ab7UM8sCfQWgdbzxkXTNVD)

Lecture Notes: https://drive.google.com/file/d/0B_urJu4cgDhMUFZiM2kwZ3pJYjQ/view?usp=sharing&resourcekey=0-GsMhHxOfzV274IDUHcR4Lg

Patreon Link: https://www.patreon.com/user?u=4354534

Видео Solving the 1-D Heat/Diffusion PDE: Nonhomogenous Boundary Conditions канала Faculty of Khan