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 :)
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
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...
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(...) + ...
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.
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
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.
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...
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.
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.?
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"
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 :)
The part when he says "Great! so, now I have solved the half of my solution..."
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
Finally, someone explained all the cases of the constant's sign and talked about the Fourier-series-related part!
After 5 years of my PDE course today I've understood this❤️ Thanks sir.
I wish my teacher made this look so simple weeks ago. Midterm in 4 hours thank you!
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
What is the concept if we write condition as Ux(0,t) and Ux(l,t)
??????????
@@besthighlights1093 The ends of the rod are insulated and the flux is zero
@@OM-wl7qe That sounds like an EE answer. In general it's just boundary conditions, could be applied to many different situations.
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!
Thank you, you helped me understand what my professors messy notes could not
Okay l can't be the only one who heard 'cup of tea ' here @2:51 .
good work, sir.
Every point is well explained, so helpful
-A student from India.
That was a surprisingly complicated solution.
By far the best explanation. Thanks a million!
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...
Praise The Sun glad it was helpful!
toooook
The best explanation ever.
Great explanation of the heat equation. Short, simple, and to the point.
Couldn't have explained this any better sir!
Thank you, this really helped me understand the concept and logic of the solution. Very clean video 👌
Thank you very much, exactly what I was looking for, great for my final year math undergrad exams
understood the entire concept just by looking at it once :)
this was so, SO well explained, thank you so so much!!!!
Thanks heaps, really helped me a lot
Thank u sir I will pray for u.love from Pakistan
Thank you best explanation, so this concept explain real times in our life for me
Looking great🎉
Thank you, math god.
excellent video I have ever watched
This was soo helpful thank you. Just learnt this concept today
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(...) + ...
Amazing explanation! Thank you so much!
after watching this i dont feel stupid anymore when looking at my PDE homework
17:42 “M for mother”.
You are my savior
phenomenal explanation
thank you very much, cannot understand it in the lecture but this video is very useful!!
Thanks, a good tutorial, very helpful
Very Clear. Thumbs up!
in minute 9:50, how do we know that the there's only one case where n=m when expanding the series?
Thank you very much, very helpful
Do you have to do the integration to find An or can you just leave it as An in your final answer?
Notice that what he got for An using orthogonality is how you find the sin fourier series for f(x)
Thanks professor
The fact that you did for case 1,2,3 looks like we need some pre-knowledge.
Thank you so much! You are awesome!
Thank you so much sir ❤️❤️❤️
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.
Great Explanation Sir😇
Thanks you sir ji,
Helped me alot.
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
He probably got imaginary numbers so you have to use euler's equation which becomes the cos and sin equation
Eurler expansion. (idk spelling) its very standard in most ode courses
U are good teacher.
Not difficult with you.
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?
yo bro chill. Its not that important
Perfect!!!! Thank you
Thank you so much 🇩🇿💕
Thank you so much for this video
top class explanation
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.
This video only contains the Homogenous Dirichlet Boundary Condition. But, yes its quite helpful.
Thanks....it's very helpful for me....
Perfect! Thanks
¡Thank you!
for case 1: Are we allowed to use Cosh and Sinh instead of "e"?
yes, it is possible, cos, we can see why not in the definition of hyperbolic functions.
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.
What is the meaning if we write condition as Ux(0,t) and Ux(x,l)
??????????????
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...
I want him to read me Green Eggs and Ham to sleep
Anyone 2024 DEC 13TH?
Thank you very much
great video!
Thanks alot .i really need wave equation can u explain it please
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.
awesome
Thank you
how would you solve for Cn if f(x) is a constant like 14
Would have been more instructive if a graphic representation of the temperature profile was given as well.
i love you
Thanks a lot!
you saved me
do you have videos on real analysis
Thnks😙
big like
case 1 , k>0
I am confused...when do we need to use lambda or lambda square
4:54
how to solve it?
There's no hope on the battlefield )=
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.
Why do the constants depend on n? Please help
It's just notation. These are subscripts.
Thanks :)
in the set of boundary conditions, will the solution change drastically if u(L,t)=T0, where T0 is some initial temperature ?
Thx
what about solution for three dimensional equation
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)
Sir wave equition with tree condition solution uplode kr dein please
thanks, u made me hate calculus
gotta say what lamda and u actually are
yo bro put the fries in the bag
Ut(x, t) - uxx(x, t) =ku??
omg such beautiful hands
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.?
Because he got the solution anyways
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"
K
thank you
Thank you