Introducing Parabolic PDEs (1-D Heat/Diffusion Eqn): Intuition and Maximum Principle

[@rubenoliveira5305]

"The proof is trivial! By now you probably used to hearing this from your incredible lazy math professors" LMAO hahahhaa so true

[@muhammadharees2225]

can you please let us know what platform do you use for handwritting your lectures on. These are amazing.

[@brendagutierrez5281]

Very helpful! Where can i find something about enrgy methods? My teacher used it for prove uniqueness to the solution of the heat equation, I need help ! Thanks

[@shadynagy1751]

I appreciate your effort , Thank you :)

[@FacultyofKhan]

Glad I could help!

[@mortezakhoshbin]

great explanation. thanks alot

[@A.Hisham86]

Fast explanation! Couldn't you be deeper than this! You became like your lazy Math Prof.

[@shadynagy1751]

Do you have any intention for videos about explanation for SPDEs ?

[@FacultyofKhan]

Stochastic PDEs? I didn't originally have that intention, but I can make some lectures if you want. Though they will probably come later on and not right now when I'm still near the start of my PDE lecture series.

[@shadynagy1751]

I think it will be so helpful as the content on web has no lectures with such explanation as you did in your series , really all interested in SPDEs or SDEs need these lectures , God blessed you Dear KHan

[@FacultyofKhan]

Thank you so much, and thank you also for the recommendation! Once I get the opportunity, I will add lectures on Stochastic DEs/PDEs.

[@javiergarcia-yy7ze]

hi, this a numerical method for solving this PDE?

[@FacultyofKhan]

This video doesn't cover any numerical methods. It's mostly to give you intuition about the Heat/Diffusion Equation. I'll probably cover numerical methods (finite difference, finite element etc) in future videos down the road though.

[@NaseerAhmad-dd6pp]

What is pde and what is 1d it is one dimension or one dimensional

[@oscarvivo1]

watch the video you will see

[@sirelegant2002]

Perfect video thank you

[@jisyang8781]

concave up.. you mean convex?

[@FacultyofKhan]

Concave up is a less ambiguous term (it just means that the curve curls up): using convex and concave makes things confusing, but yes, concave up = convex when looking up from the bottom.

[@jisyang8781]

@@FacultyofKhan First thing first. I greatly appreciate you producing these excellent videos. But I strongly disagree that 'concave up' is less ambiguous than just saying 'convex'. I think doing this contributes to more confusion in the long run. What is 'up'? Is it the line? or the bulge? If you want to attach 'up'/'down' to be more descriptive, please don't use 'concave' or 'convex', both of which has precise definition already. Instead, 'curls up' or 'curls down', like you said, is better. I prefer 'bulges down' or 'bulges up' because you can use them to describe concavity/convexity of surface as well. BTW, in your video, you already have drawn a graph, so there is zero confusion when you describe convexity of graph. Using just convex/concave (without up/down modifier) doesn't make your video more ambiguous..

[@issaomar5698]

It should not matter really. He is doing a great job outlining the basics. On my part: I can not do a half of what he is doing.

[@vidarahmatnejad394]

@@jisyang8781 It is not confusing as it is just an introduction to the concept. And the audience could learn the exact definitions later when they have a deeper look at the topic (if needed at all). Btw, Faculty of Khan, you are doing a great job, thank you!

[@jisyang8781]

@Vida Rahmatnejad Yes, it is confusing. In fact, it is so confusing that Faculty of Kahn needed to invent 'concave up'/'concave down', which then contributes more to the confusion. (What is 'up' then? line? bulge?) All I'm saying is to use right terms if they already exist. You don't casually intermix 'left' and 'right'. do you?

[@tiagoinenglish]

Oh, I think didn't understand the maximum principle :(

[@curtpiazza1688]

Interesting!

[@saraism4557]

Very hard