PDE | Heat equation: intuition

An introduction to partial differential equations.
PDE playlist: www.youtube.com...
Topics:
-- intuition for one dimensional heat (or diffusion) equation, described as a model for the diffusion of heat in a thin metal rod

[@andrekoscianski]

Holy cow. This is a needle in the haystack - there are tons of awkward explanations for this equation. Thank you.

[@ecartusciello11]

Explained more in 8 minutes than my professor did in 2 days. Thank you!!

[@powertube5671]

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.

[@jiangtao3704]

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!

[@Kinnishian]

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

[@RTran429]

Where is the next video that corresponds to this video?

[@chesterVonWinchester]

your pde videos are great. I'm so glad you're doing the Heat EQ!

[@naughtybrat94]

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.

[@theMambo90]

i've just got what i didn't in 4 years of university! great job man!

[@quantummath]

Lovely video! ... looking at the problem "intuitively" is almost Always a plus. Greetings from Hamburg.

[@deashehu2591]

You deserve a medal Sir! Having the intuition I can rock numbers!

[@josephbarnes3596]

Best explanation on the internet

[@Jhev1000]

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?

[@Postermaestro]

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.

[@cooleslaw]

Thank you, was struggling to understand but the rod analogy was perfect.

[@AustinCousineauEE]

Thank you for the amount of effort you put into these videos, great work!

[@marcosmartinezwagner8505]

You made me not hate differential equations, and thats a lot, thanks!

[@architbhardwaj5125]

that gave a very good intutive idea... thanks a lot !

[@kevincramer8330]

This is great. Thank you very much!

[@TedHadges]

Fantastic video. Thank you

[@PuleMC]

Impressively easy to understand with that explanation🤭thank you🤝

[@jeremiadumpling6333]

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!

[@rothr92]

Thanks so much, this really helped a lot

[@felixbloomington7734]

Nice video! Good work and thank you for your efforts

[@aRollingStone89]

Please make more videos on the heat equation. :D Black-Scholes would also be great!

[@ngc2440]

thanks for a fantastic work on pde. more videos are coming right? Is this the last video (so far)?

[@mouhamadouhadydiallo6863]

Great ! clear explaination...! Thanks you Sir

[@MathsOnlineVideos]

Incredible! Well explained!

[@mignik01]

brilliant. think you are getting close to non linear PDE.

[@yeast4529]

If the change in temperature is proportional to the concavity, then why do the points of inflection change temperature?

[@christianribback46]

very clearly explained! great video

[@gourabmukherjee9443]

Thank u so much..u made the entire thing clear without indulging in huge mathematical proofs...kudos..

[@rhumeetsinus]

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!

[@nathanaelgreenaway]

Excellent, excellent video, thank you so much

[@jaimes6152]

Thank you so much!

[@imnumber142]

such a calming voice

[@frizzleskillet18]

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.

[@frizzleskillet18]

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.

[@endremoen6813]

I think there is a h missing in the denominator of the definition of the derivative

[@Davidss908]

thank you so much I appreciate your clarity and quality of video

[@mio68df]

that's dope. good video

[@joangonzalvez9865]

Great series of videos on PDE!

[@rabiimughal9287]

Good job really it helps a lot

[@lizat5885]

Thank you so much! This really helped clarify the signs and also let me get away from just the textbook formula.

[@kirpagarg357]

Thankyou so much.. you made my day 😊

[@turboleggy]

Could you please make a video for deriving the equation?

[@a7x52]

does the radius of the rod affect the diffusion of the heat?

[@jennylee8570]

awesome video, thanks!

[@beautyreveal1715]

What does U represent in this equation

[@sergiolucas38]

amazing video, thank you :)

[@95MarioKaci95]

Hi can you please tell me what book u used to study PDE's???

[@m3sman121]

amazing thanx alot

[@avtaras]

Thank you, life saver!!!

[@chivoronco4853]

Good i will use and give credid to you.

[@muhammadsaad3836]

Great video

[@eliyahomar]

Thank you

[@ngc2440]

will you teach stochastic differential equations too, please?

[@veronicaecheverria594]

Is there anyone who has a video on the heat equation with gamma changing with position???

[@isaacwolf2806]

Really helped my understanding, thanks!

[@kevinw6237]

Nice intuition! I can't wait for the sequal!!! Please!!!

[@debendragurung3033]

Good for you And i need a prequel of prequel of prequel

[@yuvrajmurali8012]

Thank you!

[@9wyn]

Thank you 🙏

[@FPrimeHD1618]

You make great video's!

[@goobtron]

Great video, but why aren't there more!

[@VinodKumar-ye7ii]

I really love it...Can u please also explain the solution of this equation

[@blifx]

now how do you do it in 4d

[@azztereris]

its so sad this is not yet popular.. well not a whole lot u can actually do bout that

[@Abuwesamful]

Thank you so much.

[@nikibl8]

Thank you! Greetings from Sofia!

[@麦泳琳]

very intuitive, thank you!

[@valeo626]

f(x,0) = lovely lady lumps at time 0

[@300483rahul]

thank u very much ...very helpfull!!

[@user-lx5qb3zk8b]

place i want the salutation of heat equation

[@abidelamohammed5684]

EVERY THING WOULD BE DONE,IF ALLAH SAID.

[@abidelamohammed5684]

SALWA

[@shaymairshed2282]

thank you