PDE 13 | Wave equation: separation of variables

[@joewilliams6790]

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.

[@stanislawzelazny7515]

+Joe Williams I second that.

[@krazycrarie]

I third that.

[@rogerarbizo1242]

I fifth that!

[@kdd271998]

I sixth that!

[@rram6062]

I seventh that!

[@AdmCornFlake]

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.

[@danielstepanov2599]

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!

[@OswaldChisala]

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!

[@oscarbruno3589]

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 KZbin!

[@khaledqaraman]

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.

[@twanstegeman]

These people are the unsung heroes of youtube and the internet in general.

[@moaz_qz]

Concise , to the point , and great explanation ! Life saver , thank you

[@abdelrahmangamalmahdy]

this is a great video , most people don't know any thing about the partial differential equations ... thank you so much

[@superphilschneider]

Nice job on this video. It's not easy making such direct and efficient online lessons. Great work!

[@majidt8007]

where is the next video , number 14?

[@someonetoogoodforyou]

This is amazing! Can't believe I only just discovered your videos! Thanks!

[@michaelmead3623]

You are a great teacher. This helped me enormously. Thank you.

[@PhantomKenTen]

where is pde14, boundary values is where the problem becomes difficult

[@LeavingCertMaths]

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

[@menteencoma]

you left us with a cliffhanger man ! you're such a tease !!

[@akthamjamaldeen8432]

love and respect for your lecture That 15min video was so much of help

[@ahmadalwahab2652]

thank u so much... u were much more helpful than my instructure...

[@rummanmuhammad927]

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..

[@aman2426]

Can someone explain how to solve the ODE of lamda=(-)w^2 where the solution comes out in sin and cosine form?

[@LeavingCertMaths]

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).

[@mohhammadscharifie5059]

no , because we said that landa is constant

[@DelphianSociety]

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.

[@Muradsahar]

@ 6:45 , how can two-equations be equal to the same constant.?

[@jameshuang9568]

This is awesome! but how do we know when we should use the form "F(x)*G(t)"and the D'Alembert's formula?

[@sunildasari4977]

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

[@zahraaa59676]

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.

[@dr.pravinvadhel4183]

Why we are taking cases for lamda ? and what about the Initial and boundary conditions?

[@JonathanReyndersGreatBanter]

Thank you, this video was a life saver!

[@shahzebali8577]

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

[@mustafaawadelseed1962]

its not because w and v must equal the same lambda .

[@elfmas]

"it's not because it's not"

[@skysea7785]

Bc the two equations have one same answer therefore lambda has to be the same

[@maldighaithir]

could you elaborate more on non-homogenous boundary condition and initial condition please?

[@ayedris55]

thank you sir. I have got benefit from your videos

[@mundella4555]

Exceptional video. Top stuff. Thanks

[@ronpearson1912]

Your hand writing is awesome

[@WahranRai]

When to use the solution in PDE 12 and PDE 13 : additive vs multiplicative Are they depending on boundary conditions ?

[@LeonUnay]

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.

[@matthewjames7513]

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 ?

[@giuseppecammarata7528]

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

[@crystalc1ear]

Thank you very much. I think I'm gonna do well on my exam

[@sholaibukun1352]

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

[@DrSlough]

Great video, just have a question. Is separation of applicable to any other PDEs besides the heat/laplace/wave equations?

[@josephbatnjana159]

Yes as long as its homogenous

[@TheRebelious123]

Very nice job. Want to see more vdo's on PDE please. Thank you a lot.

[@manuelsojan9093]

Does it matter if you set the equations to -lambda as opposed to lambda? Why do some textbook use -lambda

[@ryanbadgerheart]

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

[@moar555]

You are a great teacher. Thank you!

[@nyahhbinghi]

What's the different between boundary conditions and initial conditions? isn't it the same thing?

[@juliusmwakichi9945]

Very helpful sir✊✊

[@henryprior2989]

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!

[@azzouzahmed7404]

Thank you so much for this amazing videos.

[@menteencoma]

@commutant just finished watching your videos on PDEs duuude, when is number 14 coming ?? Are we getting examples with boundary conditions next ??

[@028_asif_mujtaba_wani_ee5]

Why we use 2nd order pde for wave equation instead of first order plz

[@Thiago-fm4qk]

But how can we find the right value of omega?

[@AlexBarnadasMorera]

Does anyone have a matlab code for this?

[@anaslahrichi]

Great explanation.Thanks.

[@ShreyDutta]

Amazing stuff. Where is PDE 14?

[@jezbeat]

How do you find basic solutions??

[@rakibrahman3914]

It was just what i needed..:D thanks

[@mignik01]

Great. Are we getting into non linear regime next?

[@totasalam7060]

love this video so much thanks alot

[@liquidstl]

in other words, since LHS = RHS, = L^2 ( lambda^2), the value of lambda must be the same in both equations.

[@haozart93]

great explanation. i was just curious isn't w^2>0 the basic solution is cos and sin whereas the w^2

[@valeriereid2337]

Excellent thank so much!

[@franknostradamus]

Many thanks :) Great video!

[@1415Khan]

This really helped,Thanks a lot (Y)

[@daohung1112]

this video is useful. I think that you are a good physics teacher. where do you live? where do you work?

[@sinecurve9999]

Good video. Nice ending question.

[@liquidstl]

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

[@ryujinryuk]

whats the difference between heat equation and wave equation ?

[@nyahhbinghi]

F

[@ryujinryuk]

@@nyahhbinghi bro this was 3 years ago, im literally not a student anymore 😂 thanks for the reply tho

[@nyahhbinghi]

@@ryujinryuk my boi

[@freesoul2677]

Thank you .. Really very helpful .

[@tomasdestefano]

This is awesome!!! Thanks!!

[@presidentevil9951]

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....

[@mignik01]

like i told you before. non linear PDE and some numerical methods would be great.

[@通辽汗国太上皇]

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.

[@5stardrill410]

isn’t that solving with L’Ambert’s Method?

[@edwinedrick5349]

Great Stuff. Thanks

[@ihtishampakhtoon5151]

great sir, sir if you solve 1 question at the end of the lecture that will make our concept strong, over the topics.

[@maithilysriharan2319]

very good one

[@oguzhanozpnar2828]

Thank you soo much.

[@WahranRai]

some confusion betweem w and omega !

[@kdd271998]

You sir, are god.

[@DerMacDuff]

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.

[@Gipsy4u]

Awesome! Thanks

[@ys5399]

thx a lot~ u r great!

[@Buzmoo]

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.

[@OswaldChisala]

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 KZbinr 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. :)

[@OswaldChisala]

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.

[@shahrilnizam25]

I wish I could understand PDE moreee

[@NabilaAisyah]

WHERE THE NEXT VIDEO? I CANT SLEEP THINKING ABOUT THE SOLUTION !!!

[@mehdimahmud4614]

hi. at the begging i want to thanks you. My question is what whill happen if lambda is complex. d(dX)/X=complex number

[@udahluser]

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

[@OswaldChisala]

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 :)

[@zainabal-salihi8859]

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.

[@SequinBrain]

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.

[@Peter_1986]

I sometimes read "sum of sols" as "sum of souls".

[@funInSun26]

Question/challenge accepted!!

[@Postermaestro]

I've seen the separation of variables trick, now I can never unsee it. Lord help me!

[@luckytm5916]

i have an exam in 2 days wish me luck

[@kimnganmai5782]

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 ?

[@WalterOverton-d5h]

Conor Square

[@dimitric3607]

this video was easy to understand until u started turning the solutions to basic solutions and linear combinations. made it confusing for no reason.

[@sickdemon9381]

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[@chiranthipoornima4793]

Thank you very much.understood it very well.❤❤❤❤