In this video, I derive d’Alembert’s formula for the 1-dimensional wave equation, based on a nice factoring trick and by using the solution formulas for the transport equation. Enjoy!
Is it an open problem or are there solutions in general? For p=1 or q=1 it seems plausible to use fourier transform in either spatial or time dimensions and then finding a solution using the convolution theorem but in other cases I'm kinda clueless...
Awesome! From thermodynamics to E&M! You'll finish the physics curriculum a few more weeks :) Will you be solving quantum gravity next time? (I may be asking a bit too much, but I'm just so impressed with your videos :)
Wow, that is interesting! You basically want y’ = y^-1, so basically if you differentiate that you should have something like y’’ = 1/y, which might be solvable? Not sure 🤔
@@drpeyam Luckily for us, someone has already solved it. Check it out: math.stackexchange.com/questions/239780/functions-whose-derivative-is-the-inverse-of-that-function Glad you liked it. Maybe make a video about it? ;)
hi payem, i was wondering if you could check my proof of something for me and see if you think its valid? if not, could you explain why its not valid? thank you
Nice wave poster
Its Waving at us.
Sea what I did there?
Oh I am shore you did.
@@mcmage5250 Pun skills maxed out
@@46pi26 :^) what do, i search for puns in every corner of the YT
"How can we figure out you." YOU WILL NEVER FIGURE ME OUT, PEYAM!
😂😂😂
Beautiful and elegant derivation! Amazing video! Congratulations Dr. Peyam!!
Very instructive as usual! Thank you Mr. Pi
Absolutely magnificent!
However I must admit that I did get a little bit lost, just after the part where you said "Alright, thanks for watching..."
😂😂😂
And when you have a constant c such as utt = c*uxx the equation is
U(x,t) = 1/2c(g(x + t) - g(x - t)) + 1/2c^2 S(x + t, x- t) h(s)ds
I think t should be ct in that case
You're right thanks
Sometimes I think, Wth is being taught at school. Why aren't people like you our teacher.
Next do it in n-dimensions lol :)
of course where n=p+q and p is the number of time dimensions and q the number of spatial dimensions
Oh, it’s very complicated actually 😱
Is it an open problem or are there solutions in general?
For p=1 or q=1 it seems plausible to use fourier transform in either spatial or time dimensions and then finding a solution using the convolution theorem but in other cases I'm kinda clueless...
There are solutions, but it’s just really long and you have to separate into odd and even dimensions
Awesome! From thermodynamics to E&M! You'll finish the physics curriculum a few more weeks :) Will you be solving quantum gravity next time? (I may be asking a bit too much, but I'm just so impressed with your videos :)
lol, probably not, but there’s something neat about this coming in 2 weeks
inb4 Pap's '
Cool wave 😁❤️ DR
If u_tt represents the vertical acceleration of any point on the wave, then what does u_xx represent?
Thank you Dr. Peyam! Can you do it for more than one dimension? I'd really appreciate
It’s not as easy as you think :O
Nice explaination ,
Please sir upload the video of "derive Kirchloff formula".
I don’t think I’ll make a video on that
@@drpeyam Can you upload a video on mean value property for heat equation??
Thanks again
I have an interesting question: is there a function which it's derivative is also it's inverse function?
Wow, that is interesting! You basically want y’ = y^-1, so basically if you differentiate that you should have something like y’’ = 1/y, which might be solvable? Not sure 🤔
@@drpeyam
Luckily for us, someone has already solved it. Check it out:
math.stackexchange.com/questions/239780/functions-whose-derivative-is-the-inverse-of-that-function
Glad you liked it. Maybe make a video about it? ;)
@@drpeyam just found his solution a few minutes ago
Yeah, I was thinking about this approach too, actually! Haha, awesome new video idea, thanks 🤗
@@drpeyam
My pleasure!
Once I saw conections between waves and hyperbolic functions
Under a wave off Kanagawa
Makes it cooler lol
Wait where does s come from. What does that variable represent?
Just the variable of integration! It technically disappears after you integrate
Hi Dr. Can you recommend me what is the best book of pde for beginner that i can learn this?
The book by Walter Strauss
hi payem, i was wondering if you could check my proof of something for me and see if you think its valid? if not, could you explain why its not valid? thank you
The Camembert formula?
Hahahahaha
since you are no stranger to analysis and PDEs, have you ever taken a crack at the Navier-Stokes equation?
I’d be a millionaire if I solved them 😂
😄🙌
:)
you forgot to write the i and j