PDE: Heat Equation - Separation of Variables

[@victorscarpes]

You know it's a great explanation when it makes you feel like you could have figured it yourself even without having studied the topic. Great job, keep it up :)

[@irfanhesem45]

The part when he says "Great! so, now I have solved the half of my solution..."

[@amyhu8119]

Thank you!!! The most cleared explanation to me! This is exactly the same way my professor solved in class and you covered everything he didn’t. Really appreciate

[@erfanroghani]

Finally, someone explained all the cases of the constant's sign and talked about the Fourier-series-related part!

[@TileBitan]

i thought u were going to copy paste the definition of An based on the fourier series but u fking proved it. you got my like sir

[@besthighlights1093]

What is the concept if we write condition as Ux(0,t) and Ux(l,t) ??????????

[@OM-wl7qe]

@@besthighlights1093 The ends of the rod are insulated and the flux is zero

[@zoasis7805]

@@OM-wl7qe That sounds like an EE answer. In general it's just boundary conditions, could be applied to many different situations.

[@couldbewrong]

I wish my teacher made this look so simple weeks ago. Midterm in 4 hours thank you!

[@AM-yn2gh]

After 5 years of my PDE course today I've understood this❤️ Thanks sir.

[@tlhomotsemoteme2423]

Okay l can't be the only one who heard 'cup of tea ' here @2:51 . good work, sir.

[@BillyBob-bo9tn]

Thank you, you helped me understand what my professors messy notes could not

[@henry32463]

your explanation on how to solve for "An" is much better than the explanation my textbook given, thank you so much for this great video!

[@Peter_1986]

That was a surprisingly complicated solution.

[@kwameadu-tekyi2414]

By far the best explanation. Thanks a million!

[@praisethesun5425]

dude my teacher said that i will never understand this if i didnt took the class, i didnt took the class and i still understand this(MA). Sharing my gratitude is the only thing i can do for u lol...

[@MathemaEducation]

Praise The Sun glad it was helpful!

[@AmNotAugust]

toooook

[@DaShiz100]

Thanks heaps, really helped me a lot

[@hgrimes816]

Great explanation of the heat equation. Short, simple, and to the point.

[@barzipori4238]

The best explanation ever.

[@IrshadCh-w3p]

Looking great🎉

[@anshutyagi4089]

Every point is well explained, so helpful -A student from India.

[@ianaranda7427]

Couldn't have explained this any better sir!

[@readerbot5967]

Thank you, this really helped me understand the concept and logic of the solution. Very clean video 👌

[@KhemTiwari-u8m]

excellent video I have ever watched

[@harrishneelamegam]

understood the entire concept just by looking at it once :)

[@simrannahar8262]

this was so, SO well explained, thank you so so much!!!!

[@benwinstanleymusic]

Thank you very much, exactly what I was looking for, great for my final year math undergrad exams

[@hannahbilbie592]

Do you have to do the integration to find An or can you just leave it as An in your final answer?

[@soichiystokazu7381]

phenomenal explanation

[@pjorgen]

Thank you, math god.

[@yolanankaine6063]

This was soo helpful thank you. Just learnt this concept today

[@ashleycasillas9490]

in minute 9:50, how do we know that the there's only one case where n=m when expanding the series?

[@sasi5585]

Thank you best explanation, so this concept explain real times in our life for me

[@juniasmoyo9049]

17:42 “M for mother”.

[@mathematical_fun_with_Sumbel]

Thank u sir I will pray for u.love from Pakistan

[@isaacafariaddo834]

Thanks, a good tutorial, very helpful

[@thej680]

I think at 20:50 there's a mistake. All the other terms except the mth term will be eradicated, so it should say Am = ... . We forgot that this was a series of A1(integral stuff) + A2(...) + ... + Am(...) + ...

[@kevinshao9148]

Amazing explanation! Thank you so much!

[@yasmeenaman4471]

Great Explanation Sir😇

[@nostalgia_1439]

10:00 I've taken an ODE class and dont really understand how you got the solution to that ODE, like I dont understand where the cos and sine come from with just a homogeneous with constant coefficients

[@KenzoKento]

He probably got imaginary numbers so you have to use euler's equation which becomes the cos and sin equation

[@dudeB15]

Eurler expansion. (idk spelling) its very standard in most ode courses

[@bentoby2123]

I want him to read me Green Eggs and Ham to sleep

[@robertoberidojr.435]

You are my savior

[@besthighlights1093]

What is the meaning if we write condition as Ux(0,t) and Ux(x,l) ??????????????

[@mouazchikhani7803]

Notice that what he got for An using orthogonality is how you find the sin fourier series for f(x)

[@Maps4346]

Very Clear. Thumbs up!

[@Skumar-rg4hd]

Thanks professor

[@COALROCK8642]

The fact that you did for case 1,2,3 looks like we need some pre-knowledge.

[@abdinasirhassan807]

Thank you very much, very helpful

[@rabikhan3596]

Thank you so much sir ❤️❤️❤️

[@josephbatnjana159]

for case 1: Are we allowed to use Cosh and Sinh instead of "e"?

[@Muradsahar]

yes, it is possible, cos, we can see why not in the definition of hyperbolic functions.

[@univuniveral9713]

Hey, you have a mistake in your explanation and solution, but you ended up with the correct answer. Correction: when you were integrating to find An, you needed a summation over m sign on the lefthand side, and a double summation over n and m on the right. Only hen can you have the need to say that the integral of sin(..mx)sin(...nx) for m!=n.

[@tejpratapgaur5801]

Thanks you sir ji, Helped me alot.

[@algorithmo134]

do you have videos on real analysis

[@mecheng94]

after watching this i dont feel stupid anymore when looking at my PDE homework

[@Danieltredway1431]

Thank you so much! You are awesome!

[@imaxzzz194]

thank you very much, cannot understand it in the lecture but this video is very useful!!

[@solomonkyeimensah3701]

top class explanation

[@ozgurhanc8153]

at 6:45 why don't we consider L=i*pi*n (making e^2*n*pi*i=1) directly, instead of checking for a diferent lambda?

[@alptugtan6599]

yo bro chill. Its not that important

[@hamishthompson1409]

awesome

[@saadmajid9912]

how would you solve for Cn if f(x) is a constant like 14

[@iamakii]

Thank you so much for this video

[@chinedueleh3045]

Perfect! Thanks

[@kirankhurshid8323]

Thanks....it's very helpful for me....

[@najwaamir3107]

I am confused...when do we need to use lambda or lambda square

[@marymurphy9600]

Thank you really helpful. How do you solve if T'' instead of T'. I understand its the same method up to about 14 minutes of this video.

[@chrisgreening9313]

great video!

[@wearytrader535]

The question I'm about to ask doesn't exactly matter, but it's marginally relevant. One of your initial conditions was: u(x, 0) = f(x) I understood that u(x, t) = f(x)g(t) So, shouldn't u(x, 0) = f(x)g(0) = f(x) => g(0) = 1? And, if g(0) = 1, then g(0) = Cn(e^(0)) = 1 => Cn = 1? However, you left Cn constant, and multiplied it by the second constant (Bn) to produce An. I know it doesn't make a difference whether or not your constant is An or Bn, but I do think we should be solving as much about the problem as possible so we have a better understanding of what's really going on...

[@مصطفىهلالعطيهنهارالزاملي]

U are good teacher. Not difficult with you.

[@jordankiara]

Perfect!!!! Thank you

[@tatendasabeka4357]

Thank you

[@omarhamdani7704]

Thnks😙

[@VictorGomez-jl3yi]

¡Thank you!

[@inessinesso6536]

Thank you so much 🇩🇿💕

[@luyangliu324]

Thank you very much

[@giovannicarmona3946]

Why do the constants depend on n? Please help

[@wearytrader535]

It's just notation. These are subscripts.

[@mr.r-ff8415]

Anyone 2024 DEC 13TH?

[@yuridoggo9075]

What if the boundary condition u(0,t)=0, but u(L,t) = T? This occurs when one end is held at 0 degrees and the other end is held at a non-zero temperature. Because of this change, all of the cases for X(x) becomes non-trivial, or so I see.

[@owenwang81]

I'm not too sure why you switched the conditions of the k for the third case but definitely the solution is right so i can't complain. For both of the first 2 cases we had positive lambda but you put -ve lambda for the third case which is very odd without a clear explanation.

[@Ammar-fq1on]

Thanks alot .i really need wave equation can u explain it please

[@ابوعثمان-ع2ه]

big like

[@howtodostuff4650]

what about solution for three dimensional equation

[@Alex-wp9oo]

i love you

[@jdobrilovich]

Thanks a lot!

[@kanakraj3198]

This video only contains the Homogenous Dirichlet Boundary Condition. But, yes its quite helpful.

[@O97-t4g]

Thanks :)

[@daohung1112]

case 1 , k>0

[@p4cmanpacm4n32]

Thx

[@Sttm35]

Would have been more instructive if a graphic representation of the temperature profile was given as well.

[@stinenorevik6115]

you saved me

[@youngcashregister8197]

in the set of boundary conditions, will the solution change drastically if u(L,t)=T0, where T0 is some initial temperature ?

[@xiii1818]

4:54 how to solve it? There's no hope on the battlefield )=

[@Corvanor]

Memorize it at this point, they repeat often in this course. We were given a formula sheet with some ODE's solved for this course.

[@munirhussainmunirhussain6080]

Sir wave equition with tree condition solution uplode kr dein please

[@eplanti]

gotta say what lamda and u actually are

[@qllonc209]

yo bro put the fries in the bag

[@nooruddin7619]

any one to say me why we take a Separable variable and there function equal to some constant.for example X'/x=T''/t=c (Constant)

[@violetnino8782]

thanks, u made me hate calculus

[@auxiruiz9624]

Ut(x, t) - uxx(x, t) =ku??

[@Muradsahar]

When you got a solution for T(t) , You could have solved for B_n constant with boundary conditions T(0) = F(x), this would have resulted in B_n = f(x) , Then solution would have been T(t) = f(x)e^(-kn^2pi^2/L^2)t. why didn't you do it.?

[@woofle4830]

Because he got the solution anyways

[@MG-od3he]

omg such beautiful hands

[@marcielalves9985]

accept the Lord Jesus Christ who has not accepted yet because He is coming back ... sanctify more and more inside and outside ... doing works worthy of repentance and leaving worldliness ... leaving the vanities the tinctures, earrings, makeup, enamels , the fashions of hair and clothes, the short and tight clothes because the Lord is Holy and we must be holy in all our way of living "1 Peter 1: 15,16"

[@zlatanibrahimovic8329]

K

[@文森特-h2n]

thank you

[@gourabbiswas2002]

Thank you