PDE 13 | Wave equation: separation of variables
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- Опубликовано: 7 авг 2012
- An introduction to partial differential equations.
PDE playlist: ruclips.net/user/view_play_list...
Topics:
-- idea of separation of variables
-- separation of variables for the wave equation (3:58)
-- summary (16:46)
I don't know who you are. But your videos are an incredibly helpful tool. Whoever you are, my PDE grade owes you a drink at the end of my semester.
+Joe Williams I second that.
I third that.
I fifth that!
I sixth that!
I seventh that!
Absolutely incredible explanation.. I love anyone who can convey seemingly complicated concepts into simple terms, and you absolutely did that with this video. Thank you.
This is by far the clearest seperable PDE video I have yet come across online. Thank you for the presentation, it was very intuitive, informative, and well within the margins of conciseness. :) Keep at it!
I know you made this video years ago but the way you explain things is so excellent that I had to subscribe after just a few minutes. Looking forward to seeing what else you have on your channel!
The answer to the last question is: NO. Lambda is a constant and must be the same for both v and w. You can verify this by considering a counterexample - mixing two different values of lambda will not satisfy the wave equation in the first place.
This is amazing! Can't believe I only just discovered your videos! Thanks!
You are a great teacher. This helped me enormously. Thank you.
where is pde14, boundary values is where the problem becomes difficult
Nice job on this video. It's not easy making such direct and efficient online lessons. Great work!
Awesome, I've been trying to understand how to solve these PDEs for a week at this point and have basically learned how to do them by memory.
And now I find this video explaining everything like 10 hours before my exam. Put this guy in trending already damn RUclips!
this is a great video , most people don't know any thing about the partial differential equations ... thank you so much
Concise , to the point , and great explanation !
Life saver , thank you
love and respect for your lecture
That 15min video was so much of help
Thank you, this video was a life saver!
Continuing, 17:55 Since lambda must be unique, it appears that we cannot "mix and match" values of lambda for solutions of the wave equation
where is the next video , number 14?
you left us with a cliffhanger man ! you're such a tease !!
These people are the unsung heroes of youtube and the internet in general.
You are a great teacher. Thank you!
thank u so much... u were much more helpful than my instructure...
Thank you so much for this amazing videos.
Exceptional video. Top stuff. Thanks
love this video so much thanks alot
This is awesome! but how do we know when we should use the form "F(x)*G(t)"and the D'Alembert's formula?
Great explanation.Thanks.
thank you sir. I have got benefit from your videos
This is awesome!!! Thanks!!
Very nice job. Want to see more vdo's on PDE please. Thank you a lot.
Many thanks :) Great video!
Your hand writing is awesome
Thank you very much. I think I'm gonna do well on my exam
6:17 Presumably this equation is meant to be valid for all t and x in the domains of w and v.
If so, then we could pick a particular value of t, say t_0 and show that c^2 v''(x)/v(x) = w''(t_0)/w(t_0) (=constant) for all x. Similarly, we could pick a particular value of x, say x_0 and show that w''(t)/w(t) = c^2 v''(x_0)/v(x_0) (=constant) for all t. The constant in both cases must be the same, since from last equation, w''(t_0)/w(t_0) = c^2 v''(x_0)/v(x_0) = constant (lambda).
Great Stuff. Thanks
This really helped,Thanks a lot (Y)
Thank you .. Really very helpful .
Very east to follow! Can you do a BVP two-dimensional heat or wave equations and complete the Fourier Series. I haven't seen this done anywhere on youtube.
It was just what i needed..:D thanks
Good video. Nice ending question.
could you elaborate more on non-homogenous boundary condition and initial condition please?
When to use the solution in PDE 12 and PDE 13 : additive vs multiplicative
Are they depending on boundary conditions ?
Great video, just have a question.
Is separation of applicable to any other PDEs besides the heat/laplace/wave equations?
Yes as long as its homogenous
Awesome! Thanks
Can someone explain how to solve the ODE of lamda=(-)w^2 where the solution comes out in sin and cosine form?
lol that was kind of anticlimactically easy for a final question. But I must give you props for these videos. I wasn't really a fan of some of them because they were a bit too 'assumptious' and not really rigorous enough, but I'm getting used to your style and I'm enjoying it now.
Amazing stuff. Where is PDE 14?
u r a real genius, 1 above all, count on my experience in judging, no matter what , truth stands firm on ur side, u r the best..
Thank you soo much.
thx a lot~ u r great!
Very helpful sir✊✊
tomorrow is my final. My true final. I will not be taking any course labeled as "math" ever again. I will take math related subjects, but nothing purely math.
our teacher for the worksheets (donno if that's a thing anywhere else) hinted to us that many questions on the final will be with the 1d wave equation, which is something many of us (if not all) can understand, because for some reason, we have no teachers who can explain a subject, and the ones who can, don't believe we ever need help because we have "great teachers". This whole year, I've been relying on youtube teachers for all of the lessons, and am finally able to understand a bit of math.
Thank you for this video. Although I am still a bit lost, but at least I can try getting my hands on it and seeing if I can do it with actual simple steps.
since it is my last math now, I would love to say, I hate math, and I hate that they had to give us the wave equation just at the very end of our course, which we (or at least I) know is always neglected.
I just hope to pass.
Solve the Poisson equation Ʌ2 = -15(x2 + y2 + 15) subject to the condition u = 0 at x = 0 and x = 3 u = 3 u = 0 at y = 0 and u = 1 at y = 3 for o
@commutant
just finished watching your videos on PDEs
duuude, when is number 14 coming ?? Are we getting examples with boundary conditions next ??
very good one
To answer the final question I would say generally no because of what we have assumed, if u(x,t)=v(x)w(t) the original pde needs to be equal to the constant of separation otherwise you won't have uxx=c^2 utt anymore, as the left term of the equation would be equal to something different compared to the right term.
However you may well be lucky and get sometimes a solution that works
Why we are taking cases for lamda ? and what about the Initial and boundary conditions?
like i told you before. non linear PDE and some numerical methods would be great.
great sir,
sir if you solve 1 question at the end of the lecture that will make our concept strong, over the topics.
great explanation. i was just curious isn't w^2>0 the basic solution is cos and sin whereas the w^2
Wow.
This is a great video
Thanks a lot sir
You are awesome
Pls sir ,
I will like to know how you got answer to your basic solution
I wish I could understand PDE moreee
Does it matter if you set the equations to -lambda as opposed to lambda? Why do some textbook use -lambda
Hey can you tell me the reason why in solving you supposed w(t) =e^omega*t while in odes we used to do it y=e^mx... Is this due to independent variables x and t or any other reason
Great. Are we getting into non linear regime next?
@ 6:45 , how can two-equations be equal to the same constant.?
Where is the next video? I cant seem to find PDE 14 ... Good stuff though, makes me wonder why im paying to be confused in lectures when when its all on here.
Thanks!
its not because w and v must equal the same lambda .
"it's not because it's not"
Bc the two equations have one same answer therefore lambda has to be the same
Question/challenge accepted!!
All the solutions talked about here are a consequence of assuming u has the form u = v(x) w(t). Yet we know the general solution is u = p(x-ct) + q(x+ct) from d'Alembert's formula. Does this mean that every solution talked about in this video, /lambda > 0, /lambda < 0, /lambda = 0 must also coincidentally have the form u = p(x-ct) + q(x+ct)?
Also why is assuming u = v(x) w(t) linked to the motion of standing waves exclusively ?
no , because we said that landa is constant
this video is useful. I think that you are a good physics teacher. where do you live? where do you work?
You sir, are god.
in other words, since LHS = RHS, = L^2 ( lambda^2), the value of lambda must be the same in both equations.
What's the different between boundary conditions and initial conditions? isn't it the same thing?
How do you find basic solutions??
Hey, great video, but at the beginning the wave equation looks awkward with the xx and tt if you first watch the video without knowing this.
I just learn the wave equation, the textbook shows general solution is f(x+ct)+g(x-ct), when I saw your video, I cannot connect to these two difference solutions.
Why we use 2nd order pde for wave equation instead of first order plz
But how can we find the right value of omega?
Ciao. At about minute 6.30-6-40 you stated that "thr only way two functions of different variables are the same is that they are constants. Could you clarify please, its not clear to me this passage. Thanks
The answer to his question has to be NO. Since the solution is predicated on the fact that both sides of the equation, which are functions of different variables are equal to one another
Does anyone have a matlab code for this?
I sometimes read "sum of sols" as "sum of souls".
huh? All this time, u did characteristics method, now ur doing separable method?
Can you please explain this?
I probably need you to create a flowchart on when to use what method.
I also will be dealing with alot of 4th order inseparable PDE equations later on....
WHERE THE NEXT VIDEO? I CANT SLEEP THINKING ABOUT THE SOLUTION !!!
hi. at the begging i want to thanks you.
My question is what whill happen if lambda is complex.
d(dX)/X=complex number
I know it's been 9 months, but I can try to answer your question (maybe). You won't run into a case where lambda is complex because lambda is the equation constant, what you might be thinking of is when omega is complex, which would be when lambda is negative ( lambda = omega^2, where lambda < 0, thus omega is some form of i). This would be like having a complex root (lambda) in your classic Second Order ODEs where your solution is in Sines and Cosines
Hi! Actually lambda might be complex. It's all dependent on the starting function (the solution, in uncertain terms). If, for example, you end up with a complex sinusoid of the form e^(iwf(t,x)) where f(t,x) is a function that validates the solution, the quotient X"(param)/X(param) would be complex valued. An application of this might be found in electrical engineering, probably for EM phasor analysis or something. Oh, and I forgot to put in, X(param) would be the complex function alluded to a second ago :)
whats the difference between heat equation and wave equation ?
F
@@nyahhbinghi bro this was 3 years ago, im literally not a student anymore 😂 thanks for the reply tho
@@ryujinryuk my boi
some confusion betweem w and omega !
I could give the answer to the final question, but I don't want to spoil it. I could say that the answer lies in the name of lambda, and that should convey enough.
i just saw your vide and it really help me alot, it just i have one equation about wave , Can you help me solve this through gmail, please ?
Please anyone can help me.. I have a project to solve the wave equation With boundary condition in water resources engineering field . Please help me.
I've seen the separation of variables trick, now I can never unsee it. Lord help me!
Why is utt=v(x)*w''(x)?
Is this always going to be true?
Also, feel free to make a more descriptive video about ''basic solutions'' at 10:50
Kinda lost me there.
Basic solutions are really just a way of generating a "unit value" type solution.
Think coefficients = 1 with the knowledge that you can transform the function at will. That's my 2-cent take on what a basic solution is, but hopefully an awesome RUclipsr out there will make this topic even clearer. If his cases bother you, just focus on how to get the solution because that's the most important thing.
Also, for the question of why u(t,x) = v(t)*w(x), he assumed that the solution(s) would be expressible in that form to ensure that the PDE could be solved by the seperable variables technique, which he used. If you wanted to become even more general by presuming that u(t,x) should be implicit in t and x (i.e. the clean v*w factorization cannot be obtained) then sure, you could go ahead and solve that system for a general function.
BUT that requires more mathematical dexterity, which is why he assumed that you should be able to find a simple class of solutions given by u(t,v) = v(t)*w(x).
Hopefully that helps. :)
I switched the variables of v and w, sorry about that lol. I should have checked the video before confirming what I wrote and posting my answer. And sorry for the TL;DR...Quora habits haha.
this video was easy to understand until u started turning the solutions to basic solutions and linear combinations. made it confusing for no reason.
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