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 :)

[@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!

[@irfanhesem45]

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

[@coltoncatalli8148]

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.

[@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.

[@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!

[@tlhomotsemoteme2423]

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

[@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!

[@Peter_1986]

That was a surprisingly complicated solution.

[@anshutyagi4089]

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

[@barzipori4238]

The best explanation ever.

[@hgrimes816]

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

[@kwameadu-tekyi2414]

By far the best explanation. Thanks a million!

[@readerbot5967]

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

[@ianaranda7427]

Couldn't have explained this any better sir!

[@mathematical_fun_with_Sumbel]

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

[@DaShiz100]

Thanks heaps, really helped me a lot

[@benwinstanleymusic]

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

[@harrishneelamegam]

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

[@hannahbilbie592]

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

[@simrannahar8262]

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

[@sasi5585]

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

[@besthighlights1093]

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

[@KhemTiwari-u8m]

excellent video I have ever watched

[@Skumar-rg4hd]

Thanks professor

[@kevinshao9148]

Amazing explanation! Thank you so much!

[@yolanankaine6063]

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

[@abdinasirhassan807]

Thank you very much, very helpful

[@COALROCK8642]

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

[@isaacafariaddo834]

Thanks, a good tutorial, very helpful

[@imaxzzz194]

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

[@pjorgensen2]

Thank you, math god.

[@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.

[@soichiystokazu7381]

phenomenal explanation

[@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.

[@tejpratapgaur5801]

Thanks you sir ji, Helped me alot.

[@mouazchikhani7803]

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

[@robertoberidojr.435]

You are my savior

[@gourabbiswas2002]

Thank you

[@hamishthompson1409]

awesome

[@Maps4346]

Very Clear. Thumbs up!

[@yasmeenaman4471]

Great Explanation Sir😇

[@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...

[@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.

[@user-wr7fb8wz4n]

U are good teacher. Not difficult with you.

[@iamakii]

Thank you so much for this video

[@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.

[@mecheng94]

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

[@ashleycasillas9490]

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

[@Danieltredway1431]

Thank you so much! You are awesome!

[@chinedueleh3045]

Perfect! Thanks

[@jordankiara]

Perfect!!!! Thank you

[@kirankhurshid8323]

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

[@solomonkyeimensah3701]

top class explanation

[@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.

[@juniasmoyo9049]

17:42 “M for mother”.

[@VictorGomez-jl3yi]

¡Thank you!

[@najwaamir3107]

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

[@rabikhan3596]

Thank you so much sir ❤️❤️❤️

[@kanakraj3198]

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

[@luyangliu324]

Thank you very much

[@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

[@inessinesso6536]

Thank you so much 🇩🇿💕

[@saadmajid9912]

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

[@algorithmo134]

do you have videos on real analysis

[@Ammar-fq1on]

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

[@chrisgreening9313]

great video!

[@omarhamdani7704]

Thnks😙

[@giovannicarmona3946]

Why do the constants depend on n? Please help

[@wearytrader535]

It's just notation. These are subscripts.

[@jdobrilovich]

Thanks a lot!

[@user-fx3dj1tg1h]

big like

[@Alex-wp9oo]

i love you

[@bentoby2123]

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

[@howtodostuff4650]

what about solution for three dimensional equation

[@user-zv2jh5fx2g]

Thanks :)

[@p4cmanpacm4n32]

Thx

[@youngcashregister8197]

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

[@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)

[@stinenorevik6115]

you saved me

[@daohung1112]

case 1 , k>0

[@munirhussainmunirhussain6080]

Sir wave equition with tree condition solution uplode kr dein please

[@auxiruiz9624]

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

[@eplanti]

gotta say what lamda and u actually are

[@violetnino8782]

thanks, u made me hate calculus

[@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.

[@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

[@tatendasabeka4357]

Thank you

[@文森特-h2n]

thank you