Maximum Principle

[@miaboruto7091]

What is the relationship between the harmonic function and the maximum value of the principle؟

[@leespence9165]

You should make videos going through the Evans book... Step by step for us slow ones. And go through some qual problems while you're at it. 😂

[@drpeyam]

This might be what you’re looking for: kzbin.info/aero/PLJb1qAQIrmmCXfuXUAt9dT1Gjy_GK89OH

[@ssdd9911]

16:21 y is it -2e instead of -2ke?

[@TheJunken2]

How is this comment two months old if the video came out today :O

[@non-inertialobserver946]

@@TheJunken2 Time traveller

[@ssdd9911]

@@TheJunken2 i found it in a playlist lol

[@BlueSoulTiger]

No-one has yet answered your question: I think you've spotted a minor error - minor because I assume constant k > 0. As to the 2-month old comment: perhaps there was another video with the exact same uri (same video ID). Or is that (literally) impossible?

[@ssdd9911]

@@BlueSoulTiger it's the same video but unlisted

[@thehardlife5588]

At 7:00, could explain more why this is a bad example as it is not continuous? Where is this not continuous?

[@juju_h10]

Is the Maximum Principle still true even if we replace the heat equation condition by ut ≤ k∆u on UT? if yes, how to prove this?

[@drpeyam]

The maximum principle is still true but not the minimum principle. Exact same proof

[@juju_h10]

@@drpeyam Thanks for replying! In the minimum principle, ut >= k∆u on UT?

[@ayodeleadedeji3051]

Hi Dr Peyam, Please you should make videos going through the PDE of mathematical physics and integral equations by R. B Guenther and J.W Lee especially those exercises involving maximum principle in section 5.2 (2,3,4,5,6). I don't know how the signs really works. Thank you.

[@drpeyam]

Omg probably not, I am not a tutoring company thanks

[@marcussuzuki4031]

Hey man. Can you please explain how to derive the Chi Squared pdf from and N dimension volume of a ball. I am looking at this wikipedia document. en.wikipedia.org/wiki/Proofs_related_to_chi-squared_distribution. You dont have to re-do the derivaiton of the volume and beta/gamma derivations. I am just not getting a -1 or something.

[@drpeyam]

I don’t know what that is

[@kmac5912]

Does anyone know how to solve for the limit for x approaching positive infinity of log base x of root x of x factorial

[@fullfungo]

One solution is to start with the inequality (x/3)^x < x! < x^x. Then root x (x/3)^x < root x x! < root x x^x. Therefore, log_x(root x (x/3)^x) < log_x(root x x!) < log_x(root x x^x). log_x(x/3) < log_x(root x x!) < log_x(x). Both the left and right logs go to 1. The proof of the first inequality can be found here: math.stackexchange.com/questions/144176/factorial-inequality-problem-left-frac-n2-rightn-n-left-frac-n3-righ

[@remlatzargonix1329]

K Mac ..I dunno, whistle the first few bars and if I know it I will sing along..😀😖🙄

[@jamesbra4410]

So are u saying we couldn't solve this with say Fourier series or Sturm Liouville theory.

[@drpeyam]

Sadly no

[@jamesbra4410]

@@drpeyam Sorry if I didn't catch it in one of your videos, but why can't separation of variables and fourier series/sturm-liouville theory work for those boundary conditions.

[@drpeyam]

Yes they can, what I’m referring to is the maximum principle cannot be shown with separation of variables

[@MathForLife]

Where is max? I am here lol Nice video!

[@drpeyam]

Hahahaha

[@drpeyam]

Hi Max!!! I miss you 😄😄😄