Thank you for the wonderful tie-in with the guitar near the end!
@fabiofarina95792 жыл бұрын
Fun fact about history of music and science. Equal temperament, the way we divide octaves in notes in multiple log_2(1/12) was rediscovered in mid1500 by Vincenzo Galilei. He's Galileo father
@Eigensteve2 жыл бұрын
Whoa, that is super cool! I didn't know that
@MajdAlmuntaser-b1x9 ай бұрын
This guy is incredible. he has helped me so much.Thank you so much
@mathhack864710 ай бұрын
Ce valeureux Professeur est génial, il a le don d'enseigner et de simplifier les concepts qu'on prenait parfois pour des citadelles impénétrables . Un grand Merci pour vous cher Monsieur . may God Bless you , I know it's hard, but. you have to publish more for the best of your thirsty and faithful audience, . Thanks,
@ravenecho2410 Жыл бұрын
for the negative sign, similar to the heat equation video, diffision was negative bc it was the state returning to equillibrium (exuding heat to the env), similarly the string will be returning to equillibrium in a non-preturbed state (at rest) at least kinda how i think of it, might help others with sign of lambdas
@thomasjefferson6225 Жыл бұрын
I like this way of thinking.
@khaledqaraman Жыл бұрын
Frequency: number of waves passing by a specific point per second. Period: time it takes for one wave cycle to complete. The relation between frequency (f) and time period (T) is given by f=1/T. Notice that (f) increases when L is shortened.
@mikebull90472 жыл бұрын
the step to eliminate the sin solution part is not clear. and the constant c is employed twice in 2 different uses- But that's nitpicking. great lecture
@Eigensteve2 жыл бұрын
Thanks for letting me know -- always good to know what could be more clear.
@ares9748 Жыл бұрын
He removed the sin part because sin(c£t) when t= 0 is equal to zero. Sin (0) = 0 . So we removed it . Because according to initial condition when t= 0 , U(x,0) = f(x).
@alengm11 ай бұрын
@ares9748 that just means that sin in G doesn't contribute to u at t=0. It still doesn't contradict the initial condition, so why remove it?
@ReaganJohnson-n5w Жыл бұрын
Excellent, truly. Thank you for posting.
@shakennotstired83922 жыл бұрын
Maybe the sin term in the general solution for G(t) should not have been dropped off? the coefficient associated with that term will be determined by a 2nd initial condition, i.e., u"(x,0).
@kingsgambit2 жыл бұрын
agreed!
@郎沛橦 Жыл бұрын
agreed! +1
@awsomeguy3291 Жыл бұрын
Yeah since it's second order we need two I.C's.
@khaledqaraman11 ай бұрын
At 28:08 he assumed implicitly that dU/dt (x,0) =0 which means the initial velocity is zero. So that's an extra initial condition that was not mentioned at the beginning.
@DaviidReiis2 жыл бұрын
TIL: fingers on guitar strings are high-pass filters
@faribabiyouki15005 ай бұрын
Thank you for the informative video.
@raphaelmoreira185023 күн бұрын
Art.
@SergeyPopach3 ай бұрын
it turned out to be that we got a vector space with orthonormal basis of infinite dimension that has infinite amount eigenfunctions and their corresponding eigenvalues… just like in quantum physics
@doc3row5 ай бұрын
Newton wanted to apply music theory to his prism spectrum. He could "see" 6 colours. Red orange yellow green blue and the darker blue that he called Violet. But diatonic scale A-G is 7 notes. So he invented "indigo" to appear between blue and violet. Musical string analogy achieved 👍
@edcoad4930 Жыл бұрын
"resonates" - very good. Comedy aside, great video.
@alibekyeskermessuly1627Күн бұрын
why didn't you use the second initial condition u'(x,0)=g(x)?
@rumeysabilcan3481 Жыл бұрын
this video is perfect🥰 thank you so much
@rakshitjoshi9322 жыл бұрын
I hope you delve a bit into seismology too :)
@Rosalies_ Жыл бұрын
Really good analysis. Would love a 2D adaptation to emphasize interactions between indices :)
@rajatsingh-te2wf Жыл бұрын
Sir, why are they called eigen values and eigenfunction. Kindly explain. Your small effort will be a great help to me.thanks
@Dawlada Жыл бұрын
I would recommend you to refer Linear algebra to understand that point. Once you understand eigenvalues it will be easy to understand eigenfunction. It is a bit tough but very beautiful.
@juancarlossanchezveana18126 ай бұрын
Amazing. Thanks
@Tom-sp3gy3 ай бұрын
You are the best ever!
@ruhulhowlader7163 ай бұрын
Professor please show me that when a unit mass as a wave propagate and transfer energy to the mass energy is kept constant. I can find particle velocity and shear strain for a shear wave and the displacement at a particular point for any time t but I don’t get the total energy of at the point does not main the same value. As shear strain is directly related to the particle velocity, is it that I have to consider either particle velocity or shear strain plus displacement related velocity in the perpendicular direction of displacement. Please help me.
@mathjitsuteacher2 жыл бұрын
Hi Steve, the last video you posted was the separation of variables one. I believe you skipped a video.
@Eigensteve2 жыл бұрын
If you go to the "Vector Calculus and PDEs" playlist, they should all be there in order.
@SarjilJawadАй бұрын
But how is it that we take the constant as -lambda^2
@pain47432 ай бұрын
Amazing, Than you
@thomasjefferson6225 Жыл бұрын
Id die of embarsmemt having someone record me playing a guitar lol.😅
@McSwagical4 ай бұрын
how do they make these videos? does the prof just write backwards???
@alexandermuller88583 ай бұрын
indeed this makes it even more next level. The explanation is in one direction but the writings are backwards
@matthewsarsam8920 Жыл бұрын
wouldn't g(t) have the cos term dropped rather than the sin?
@الصوتالرخيم2 жыл бұрын
I wish i have your knowledge
@Eigensteve2 жыл бұрын
Keep watching and you will!
@kritb33452 жыл бұрын
Would lambda be the eigen vectors and Bn be the eigen values? When I imagine an infinite sum of frequencies forming a solution, I think of each frequency as the eigen vector and Bn is the correct weight. I may be confusing eigen vectors for Fourier basis functions...
@rajinfootonchuriquen Жыл бұрын
A linear combination of eigenvector don't need to be weigthed by its eigenvalues. In this case, the sines are eigenvector or "eigenfunction" of the differential operator, lambdas are the eigenvalues, and the Bs are the unique weights that can form the initial distribution with the fourier series.
@Tyokok2 жыл бұрын
Steve, why you call lambda square Eigenvalue? How does this relate to matrix Eigenvalue? Thank you so much again for such vivid elegant explanation of wave equation video!
@rajinfootonchuriquen Жыл бұрын
If you think of a differential operator D, applying to a function and setting a eigenvalue problem is: D(y) = a*y where "a" is a scalar and "y" is a real-value function. Solving for "y" gives y=e^(ax), so you can see that e^(ax) is an eigenvector or "eigenfunction", meanwhile "a" is it's eigen value. In this case, the eigenvalues are infinitly many because it's a partial differential equation, meaning that it's has infinite solution. In a normal ODE, has finite many of them, so there is finite quantity of solutions.
@Tyokok Жыл бұрын
@@rajinfootonchuriquen WOW! clear! Really appreciate it Daniel!
@rajinfootonchuriquen Жыл бұрын
@@Tyokok your welcome :)
@Tyokok Жыл бұрын
@@rajinfootonchuriquen this is real fun stuff
@rajinfootonchuriquen Жыл бұрын
@@Tyokok yeah agree 🤓
@kelvinadimaswijaya9523 Жыл бұрын
12:35 any specific proof of why it's equal to constant?
@batu9049 Жыл бұрын
hey hello it not need proof that space cant equal time at there like 5x is not equal to t or 5t or something it just can be if they equal a constant
@rajinfootonchuriquen Жыл бұрын
The only function which can acept non related argument is the constant function, because the other case is for any f, g: R to R such that f(x) = g(y), means that x = f^-1(g(y)) or viceversa, which can't be because x and y are not related by any function.
@MisterTutor20108 ай бұрын
Fouier Transform or Series?
@drumeophile7 ай бұрын
I thought the same
@rajinfootonchuriquen Жыл бұрын
Me costó entender que "buzzcard" se refería a "buscar".
@ploopsie14039 ай бұрын
what is Cn?
@lt43769 ай бұрын
30:12
@ploopsie14039 ай бұрын
@@lt4376 thanks!
@AminSatlikh2 жыл бұрын
The solution of wave eq. is too ugly here and it presented in a weak way. There are far better and cleaner ways of defining the solution analytically! Such a pity!
@kelvinadimaswijaya9523 Жыл бұрын
well, suggest one then
@rajinfootonchuriquen Жыл бұрын
What is the ugly or weak?
@AminSatlikh Жыл бұрын
@@rajinfootonchuriquen The way of presenting the solution in comparison with others who did the same. Up to this point, almost everything was smooth and pretty. I think he needs to improve it.
@declanwk1 Жыл бұрын
this is a brilliant presentation by a master teacher. He has put so much work into it and then gives it to the community for free. He deserves our respect
@enginbolat61238 ай бұрын
Can you solve this question? I couldn't solve it. Can you help me? Find the distribution 𝑢(𝑥, 𝑡) by writing the wave equation and boundary conditions for a rod (one dimension) of length L=1 unit, with both ends fixed and whose initial displacement is given by 𝑓(𝑥), whose initial velocity is equal to zero. (𝑐2 = 1, 𝑘= 0.01) 𝑓(𝑥) =ksin(3𝜋x)
@HosRo4161 Жыл бұрын
"Harmonics of the planets" is real -- "Kirkwood Gaps" (en.wikipedia.org/wiki/Kirkwood_gap) :)