Excellent! It's much easier to explain in one dimension, then the partial in one dimension can be replaced with the Laplacian which makes it valid for three dimensions. Also, you are also easy to listen to. Good flow and good pace.
Thank you! I feel like in lecture I (at best) follow the language as it's logically consistent. But here I feel like I have an actual understanding. So thank you for the effort put into these videos
I think the PDE series, even the heat equation part, are not over yet, such as laplace equation isn't mentioned. hope you can make them up, that will be a great contribution for popularizing PDE. BTW, you have done a very great job!
In the end of the video you said there will be a derivation of the heat equation. I couldn't find any derivation of it in your channel. I request you to share the video if possible because you have explained it well.
Great video! I shared one of these explanations with my class. I linked to this video in a pinned comment. Did you ever get around to deriving the heat equation from the conservation of energy principle?
The layout of "Some new topic: Intuition" into "Same topic: derivation" is extremely pedagogical. Hope you're still teaching somewhere. You should really get in touch with Khan Academy to reach a big audience. This sort of material is invaluable.
I’m not sure if I have a wrong understanding, but online I’m finding many videos solving for the heat equation, but how do you actually find the temperature of a point x at time t?! Also what is the temperature measured in? Joules? I’m just looking for a way to actually use the equation. Very helpful video by the way!
Hi... Thanks for the explanation! I'm confused about the general solution though. I understand the math behind the derivation, but I don't understand the physical interpretation. In my book, it says that the value of the solution is a kind of weighted average of the initial values around the point x. How does this follow from the integral of the source function and the initial condition, and your animation? Please help!
Maybe I'm misunderstanding. He said the graph is a snapshot of the spatial temperature distribution (what the temperature looks like as a function of space at one instant in time). But when he explains the graph's shape he says "let's see how this temperature changes in time". He's using a temperature versus space graph to explain how the function evolves in time? How does that make sense? Feel like I'm missing something here. I'm a dummy so an explanation would be amazing. Thanks Bois.
Oh I think I understand. He's using the second derivative of the graph and showing how it relates to time. Because the equation literally says that the second derivative of the function with respect to space is equal to the first derivative of the function with respect to time. Gonna leave this here in case anyone else is ever confused about the same thing.
Holy cow. This is a needle in the haystack - there are tons of awkward explanations for this equation.
Thank you.
Explained more in 8 minutes than my professor did in 2 days. Thank you!!
Excellent! It's much easier to explain in one dimension, then the partial in one dimension can be replaced with the Laplacian which makes it valid for three dimensions. Also, you are also easy to listen to. Good flow and good pace.
Thank you! I feel like in lecture I (at best) follow the language as it's logically consistent. But here I feel like I have an actual understanding. So thank you for the effort put into these videos
I think the PDE series, even the heat equation part, are not over yet, such as laplace equation isn't mentioned. hope you can make them up, that will be a great contribution for popularizing PDE. BTW, you have done a very great job!
Where is the next video that corresponds to this video?
your pde videos are great. I'm so glad you're doing the Heat EQ!
You deserve a medal Sir! Having the intuition I can rock numbers!
Thank you for the amount of effort you put into these videos, great work!
i've just got what i didn't in 4 years of university! great job man!
In the end of the video you said there will be a derivation of the heat equation. I couldn't find any derivation of it in your channel. I request you to share the video if possible because you have explained it well.
Lovely video! ... looking at the problem "intuitively" is almost Always a plus.
Greetings from Hamburg.
Best explanation on the internet
Thank you, was struggling to understand but the rod analogy was perfect.
Great video! I shared one of these explanations with my class. I linked to this video in a pinned comment.
Did you ever get around to deriving the heat equation from the conservation of energy principle?
You made me not hate differential equations, and thats a lot, thanks!
Impressively easy to understand with that explanation🤭thank you🤝
The layout of "Some new topic: Intuition" into "Same topic: derivation" is extremely pedagogical. Hope you're still teaching somewhere. You should really get in touch with Khan Academy to reach a big audience. This sort of material is invaluable.
I’m not sure if I have a wrong understanding, but online I’m finding many videos solving for the heat equation, but how do you actually find the temperature of a point x at time t?! Also what is the temperature measured in? Joules? I’m just looking for a way to actually use the equation. Very helpful video by the way!
What does U represent in this equation
Thank u so much..u made the entire thing clear without indulging in huge mathematical proofs...kudos..
I think there is a h missing in the denominator of the definition of the derivative
does the radius of the rod affect the diffusion of the heat?
Hi... Thanks for the explanation! I'm confused about the general solution though. I understand the math behind the derivation, but I don't understand the physical interpretation. In my book, it says that the value of the solution is a kind of weighted average of the initial values around the point x. How does this follow from the integral of the source function and the initial condition, and your animation? Please help!
thanks for a fantastic work on pde. more videos are coming right? Is this the last video (so far)?
will you teach stochastic differential equations too, please?
If the change in temperature is proportional to the concavity, then why do the points of inflection change temperature?
They don't notice the inflection points are marked with a dot at 3:40
Nice video! Good work and thank you for your efforts
Could you please make a video for deriving the equation?
Maybe I'm misunderstanding. He said the graph is a snapshot of the spatial temperature distribution (what the temperature looks like as a function of space at one instant in time). But when he explains the graph's shape he says "let's see how this temperature changes in time". He's using a temperature versus space graph to explain how the function evolves in time? How does that make sense? Feel like I'm missing something here. I'm a dummy so an explanation would be amazing. Thanks Bois.
Oh I think I understand. He's using the second derivative of the graph and showing how it relates to time. Because the equation literally says that the second derivative of the function with respect to space is equal to the first derivative of the function with respect to time. Gonna leave this here in case anyone else is ever confused about the same thing.
that gave a very good intutive idea... thanks a lot !
Hi can you please tell me what book u used to study PDE's???
This is great. Thank you very much!
now how do you do it in 4d
Is there anyone who has a video on the heat equation with gamma changing with position???
brilliant. think you are getting close to non linear PDE.
Please make more videos on the heat equation. :D Black-Scholes would also be great!
Fantastic video. Thank you
Thanks so much, this really helped a lot
Incredible! Well explained!
Thankyou so much.. you made my day 😊
Great ! clear explaination...! Thanks you Sir
such a calming voice
Thank you so much! This really helped clarify the signs and also let me get away from just the textbook formula.
Great video, but why aren't there more!
thank you so much I appreciate your clarity and quality of video
Great series of videos on PDE!
Good job really it helps a lot
very clearly explained! great video
Thank you so much!
awesome video, thanks!
I really love it...Can u please also explain the solution of this equation
that's dope. good video
amazing video, thank you :)
Excellent, excellent video, thank you so much
Great video
its so sad this is not yet popular.. well not a whole lot u can actually do bout that
Imagine heat from a candle. That heat is represented as a physical heat form.
Thank you, life saver!!!
Thank you 🙏
amazing thanx alot
Good i will use and give credid to you.
place i want the salutation of heat equation
Thank you!
You make great video's!
Really helped my understanding, thanks!
Nice intuition! I can't wait for the sequal!!! Please!!!
Good for you And i need a prequel of prequel of prequel
thank you
f(x,0) = lovely lady lumps at time 0
my humps f(x)
Thank you! Greetings from Sofia!
Thank you so much.
very intuitive, thank you!
Won't sleep my voxels aee shaky
EVERY THING WOULD BE DONE,IF ALLAH SAID.
thank u very much ...very helpfull!!
SALWA
Thank you