hi dr peyam iam not commenting youtube too much but your videos and you are so energetic and very helpful.Thanks for sharing them in youtube! great days
Very nice. Math just flows from you without pain. Re the moral of this video: In "other" words (from a physics-ish point of view), THERE ARE NO "STANDING WAVES" OF HEAT, (as there occasionally are with electricity and magnetism).
1:23 "Insulate the boundaries"!? As a physicist I know that in order to keep a temperature of a certain point at 0K you continuously need to milk all the heat out of that point and you can only do that when it's not insulated, because insulation means barricading heat transfer.
Hello Dr. Payam, thank you so much for your great videos. You mentioned that there exist some videos related to your research. Where can I find them? Thank you!
How would you formally justify interchanging the derivative and integral operators? Also, if U=0 then isn't there a problem with multiplying by it at the start?
Multiplying by 0 is not a problem, everything is valid. And you can use the dominated convergence theorem, after replacing the derivatives by difference quotients
Is there some more general energy method? Using heat kernel expansions of functions to see how the energy flows kind of thing? Just curious. Learning all the particulars of Guassian distributions from a thermo point of view is good :) Also, I know it is different in many ways, but this topic reminds me of Ricci Flow. Sweet. LvYrChn4vr!
I'm really liking this PDE series
Thanks 😊
hi dr peyam iam not commenting youtube too much but your videos and you are so energetic and very helpful.Thanks for sharing them in youtube! great days
Definitely appreciating the higher level maths
Have you seen Heavisde's approach to the heat equation? It's quite outrageous; he uses fractional calculus.
Do you have a reference?
@@tosifahamedPage 261 of "AN INTRODUCTION TO THE FRACTIONAL CALCULUS AND
FRACTIONAL DIFFERENTIAL EQUATIONS" by K S Miller and Bertram Ross.
AH! I was thinking almost everywhere then you said it and it made me so happy :D
Hello Dr Peyam, I love the way you talk and teach; you break things down easily. Please upload a video where you solved an example. Thank you
Thank you very much.
Very nice. Math just flows from you without pain.
Re the moral of this video: In "other" words (from a physics-ish point of view), THERE ARE NO "STANDING WAVES" OF HEAT, (as there occasionally are with electricity and magnetism).
1:23 "Insulate the boundaries"!?
As a physicist I know that in order to keep a temperature of a certain point at 0K you continuously need to milk all the heat out of that point and you can only do that when it's not insulated, because insulation means barricading heat transfer.
Thank for teaching!!!
Hello Dr. Payam, thank you so much for your great videos. You mentioned that there exist some videos related to your research. Where can I find them? Thank you!
Check out my 100th video special!
How would you formally justify interchanging the derivative and integral operators? Also, if U=0 then isn't there a problem with multiplying by it at the start?
Multiplying by 0 is not a problem, everything is valid. And you can use the dominated convergence theorem, after replacing the derivatives by difference quotients
Nice 👍
Is there some more general energy method? Using heat kernel expansions of functions to see how the energy flows kind of thing? Just curious. Learning all the particulars of Guassian distributions from a thermo point of view is good :) Also, I know it is different in many ways, but this topic reminds me of Ricci Flow. Sweet. LvYrChn4vr!
hello, please i have to ask is k>0 ? because if it is not we can't deduce that the derivative is negative , or am i missing something ?
k > 0
Can anyone tell me , why we have to multiply 'u' on both side before integrate?
Dr. Peyam what happened with blackpenredpen? Why he is not active?
He’s completely fine, just taking a break
First I think
2nd comment
The thumbnail is cursed math