Gaussian Integral 3 Differentiation

[@shiina_mahiru_9067]

The light turns off --> (sound of some sleeping gases) --> Peyam falls down --> the story of the Gaussian Integral and Dr. Peyam . . . . . . to be continued

[@MrCigarro50]

Esta serie es simplemente fascinante...Gracias Dr. Peyam.

[@waterfirecards5128]

In 6:30 how did you get from the first line to the second? And how can you just take away the d/dt away from the integral?

[@alichowdhury3502]

Notice derivative of first line is second line. It is effectively doing the partial derivative with respect to t.

[@waterfirecards5128]

Ali Chowdhury yes but then how did he just move out the d/dt away from the integral?

[@alichowdhury3502]

WaterFireCARDS by Leibniz Theorem. So he took the partial derivative with respect to t and the took out the derivative.

[@rajatkhandelwal7276]

Sir plz change the angle of the camera.

[@drpeyam]

Ok

[@cheshstyles]

@@drpeyam from ~peyam over 6 to ~peyam over 3 Still love your videos tho!

[@michelkhoury1470]

Very nice solution... I solved this famous integral using gamma function.

[@mihaipuiu6231]

I like very much Dr. Peyam , because ...1.He knows Math., and 2. He has a lot of charisma. Good for You!

[@Rundas69420]

The best way of calculating integrals: Go in the opposite direction xD. Now I wonder whether you can find derivatives using integrals. Would be fun though. For some people at the university where I study maths, saying something like "plugging in t=infinity" would be considered some kind of mathematical mutilation. Germans can be weird sometimes :D.

[@Xrelent]

You should check out FlammableMaths. He does a lot of Feyman integration :)

[@Rundas69420]

@@Xrelent I already know this boi and his nice videos. Thanks for the recommendation anyways man :D

[@ashwinvishwakarma2531]

kind of hard to see the board from this perspective

[@kqp1998gyy]

I suggest to use the left side only and flip between the inner and outer board.

[@srpenguinbr]

Very neat solution!. When I saw the title, I had the idea of using Feynman integration with a(t)=int from 0 to inf of e^-ax^2dx if you differentiate and solve the separable diff eq (a'(t) can be expressed in terms of a(t)), you can easily get an explicit expression in terms of t. However, I wasn't able to think of a nice value of t to plug in as an attempt to solve for the constant. So I think it does not work

[@drpeyam]

Next video :)

[@holyshit922]

Infact he used Leibniz rule in reverse

[@lakhdarhaouassi4948]

13 minutes sont inoubliable. merci

[@paulbooer7171]

Really interesting. I may have to watch it 5 times before I get it. It is like magic.

[@michelkhoury1470]

But I think we use Lebesgue theorem not because integral of 0 is not necessary 0 but because to switch limit and integral sign

[@patricksalhany8787]

Yeah, to justify that lim(integral)=integral(lim).

[@TieJote]

Thats what he said, dominate convergence theorem. Now i am not sure if lebesgue theorem is an alternate name, but Peyam said correctly what theorem he used.

[@patricksalhany8787]

It is called dominated convergence theorem, or Lebesgue's dominated convergence theorem.

[@drpeyam]

Yep, that’s what I meant

[@michelkhoury1470]

@@TieJote yes you're right they are the same

[@sugarfrosted2005]

I legitimately thought to ask if you were using his notes.

[@liyi-hua2111]

9：58 If you let t equals to zero then the second integral will not be exist since you have divided by t in your calculation. Or should this method be presented as lim-to-infinity form to be more specific

[@TheGeneralThings]

From 12:54 onwards, my jaw dropped to the floor. That was so satisfying to watch!

[@michaelbaum6796]

Nice solution👍

[@adityavarshney7189]

The betrayal at 3:30 when he says he's gonna use u-sub but instead uses y xD

[@MathematicIsFun]

The board is impossibly small and invisible on the right. Can you please change the angle of your camera?

[@drpeyam]

Ok

[@xy9439]

This was the way I was shown in class for the first time actually

[@GoravKumar-cm5dz]

Dear sir 1+2+3+4+5+6+7=-1/12 how please expand

[@drpeyam]

Outrageous divergent series kzbin.info/www/bejne/bITYl5ZodsSFe8k

[@boukharroubamediane119]

Wonderfully solved by calculus😊👍. The perspective shooting is convenient too👍

[@YOUSIFPOTATOYT0]

Can you make the camera nearer to the white board next time

[@drpeyam]

Ok

[@jacoboribilik3253]

Holy cow, good proof

[@wolframalpha8634]

Hey!!Dr.Peyam!!

[@PackSciences]

Didn't know that one, interesting 👍.

[@juanjuan-mi4gi]

Integral e-x3 ?....

[@orangeguy5463]

AMAZING! This is the first one that really blew my mind with its elegance. Great proof, thanks for sharing!

[@shanmugasundaram9688]

The very same method used to calculate the integral of sin x^2 from 0 to infinity.

[@drpeyam]

Yes, I posted a video on that

[@snejpu2508]

press 5. : )

[@maxwellsequation4887]

5

[@catholic_zoomer_bro]

One Gaussian boi

[@tehyonglip9203]

Nice T-shirt

[@Debg91]

So far we have always ended up with the integral squared 🤔

[@jibran8410]

weird flex but ok

[@jonasdaverio9369]

I really like 60 fps

[@shandyverdyo7688]

Wow.

[@がつかくん]

:D