PDE | Heat equation: intuition

An introduction to partial differential equations.

Topics:
-- intuition for one dimensional heat (or diffusion) equation, described as a model for the diffusion of heat in a thin metal rod

[andrekoscianski]

Holy cow. This is a needle in the haystack - there are tons of awkward explanations for this equation.
Thank you.

[ecartusciello]

Explained more in 8 minutes than my professor did in 2 days. Thank you!!

[powertube]

Excellent!  It's much easier to explain in one dimension, then the partial in one dimension can be replaced with the Laplacian which makes it valid for three dimensions.  Also, you are also easy to listen to.  Good flow and good pace.

[Kinnishian]

Thank you! I feel like in lecture I (at best) follow the language as it's logically consistent. But here I feel like I have an actual understanding. So thank you for the effort put into these videos

[jiangtao]

I think the PDE series, even the heat equation part, are not over yet, such as laplace equation isn't mentioned. hope you can make them up, that will be a great contribution for popularizing PDE. BTW, you have done a very great job!

[deashehu]

You deserve a medal Sir! Having the intuition I can rock numbers!

[chesterVonWinchester]

your pde videos are great. I'm so glad you're doing the Heat EQ!

[theMambo]

i've just got what i didn't in 4 years of university! great job man!

[quantummath]

Lovely video! ... looking at the problem "intuitively" is almost Always a plus.
Greetings from Hamburg.

[cooleslaw]

Thank you, was struggling to understand but the rod analogy was perfect.

[marcosmartinezwagner]

You made me not hate differential equations, and thats a lot, thanks!

[RTran]

Where is the next video that corresponds to this video?

[AustinCousineauEE]

Thank you for the amount of effort you put into these videos, great work!

[naughtybrat]

In the end of the video you said there will be a derivation of the heat equation. I couldn't find any derivation of it in your channel. I request you to share the video if possible because you have explained it well.

[architbhardwaj]

that gave a very good intutive idea... thanks a lot !

[rothr]

Thanks so much, this really helped a lot

[lizat]

Thank you so much! This really helped clarify the signs and also let me get away from just the textbook formula.

[PuleMC]

Impressively easy to understand with that explanation🤭thank you🤝

[Jhev]

Great video! I shared one of these explanations with my class. I linked to this video in a pinned comment.


Did you ever get around to deriving the heat equation from the conservation of energy principle?

[Postermaestro]

The layout of "Some new topic: Intuition" into "Same topic: derivation" is extremely pedagogical. Hope you're still teaching somewhere. You should really get in touch with Khan Academy to reach a big audience. This sort of material is invaluable.