at 9.26 it is dtheta instead of dx , I think.

Why can’t all professors be just like this

how do you generalise to evaluate zeta(4) with integrate_0^1 1/(1-xyzw) dx dy dz dw --> Pi^4/90?

Amazing explanation!

GOAT change of variable is amazing! Its logic would be simpler if defining (x=sinu/sinv, y=cosv/cosu) in a triangle 0<u<v<Pi/2. Salute!

At 1:29:06 why is the 2nd row 1st collumn a 1 and not a 2? 2yw = 2*1*1=2 isnt it?. still Thank you for a great video overall ,helped alot :).

But the mapping of domain to codomain ( or vice versa) seems very strange and hard to understand.(for example What would be the value of (u,v) when x=0,y=0). It is not one to one mapping. Thus the equality of integration (with Jacobian factor ) can still hold true?

I took E. Giroux course about Geometry and PDEs last year, I was not expecting to see him in this video.^^

Dont give me a metric ❤❤

can someone explain the triangle thing to me please and what would the new bounds be?

Did you catch Grant Sanderson's (duet) piece on "Twin Primes". That's the rarefied atmosphere in which you're flying. For a guy who's probably busy with math research, your musical talents are just frosting on the cake. This would be a richer experience for me if I knew the artist you're satirizing.

Joe you are great 😂❤❤

nice

Actually perfect!

Thank you. This video helps a lot.

This was super useful! thank you!!!!!

Brilliant video, thank you!

i am so luckily that i found this video. Thanksss.

good shit man

i have never seen such good solution with so nice quality for basel problem , thank you and keep making math videos

Hello

Thank youuuuuu

nice

Massive throwback. Feel's like just yesterday I was struggling to calculate the flux. How is this not #1 on Trending...

😭 'promosm'

Love how this video takes the strees out of the topic and expresses it with such clarity and empathy of understanding. Thanks!

Man, loose the background music!

I tried the double integral with partial fraction and it is a nonelementary integral.

Man, you just saved my life. I was really struggling with building up understanding about what was behind the IFT and really couldn't wrap my head around its generalization to higher dimensions. Thank you.

the memories this brings back... thank you joe!

new video from the best artist >w<

I've been too busy as of late to make much music or edit videos, but I've dug up some old nearly finished projects and demos to share

Exactly what I needed. Thanks!

Amazing

when you did the substitution of du=-sinxdx, the negative sign change the sign in each term of the solution.

What the holy actual F??? You made this insanely easy to understand and this trick is awesome.

i figured quickly that lnx<sqrt(x) so the sum cant be bigger than zeta of 1.5 which converges, and if anything ucan still work out of the very first term or 2 are smaller or equal but ye

now this is the peak of the music industry

😂😂 great ❤

Absolutely Brilliant! The substitution is simply Mind-blowing!

Marvellous solution... just the best solution to the Basel problem..

Bullshit!

Ridiculous.

Vert nice

😮

THANK YOU SO SO SO MUCH!!!!

Lmao 😂😂😂

Very nice video 🤟😄 Very clear explanation 😊

So what we have here, in example 2, is a vector field that is *not conservative, and we still get zero work? Is this because of the "hole" at the origin?

Me thinks a linear algebra playlist in the same vein would be good.