Solving the 1-D Heat/Diffusion PDE by Separation of Variables (Part 2/2)

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In this video, I continue the solution to Part I of the lecture. There's an important use of the Sturm-Liouville Theorem along with some algebraic manipulations to arrive at the final answer, which is an infinite series.

Questions? Let me know in the comments!

Liked the video? Despised it? Tell me that in the comments as well.

Prereqs: My PDE series up till this point, basic ODEs, and the Sturm-Liouville Theorem I made a video about.

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Straightforward, relaxed, intuitive - perfect.
That's how you do a real math video.

Peter_

So this is what my textbook was trying to explain. Thank you! I also appreciate the pace in your videos! Don't have to watch at 2x like with other videos. :D

dapinpinj

I was trying to follow the Sturm-Liouville eq as I've never learned it then I realized after you apply it you just end up with a simple fourier transform which is how I was taught to solve these. We just apply the fourier directly where an = int ( F(x)*Sin(npi/L))

soccercubeing

My tutor is a great person, but mb just not the best tutor. Even though she's trying to bother us to learn. So anyway, I'm trying to understand this topic by myself, and your work is perfect for this. Thank you!

now_ever

Our chemistry teacher in high school showed us this but never bothered to explain it more detailed, which was pity.... Thanks for the good and informative series on the topic!

CossZt

You are the best I really had a big problem in PDE but you solve it very easy thanks for Lecture notes which you have linked they are very effective and helpfull for learning I liked all of your videos for PDE from first up to here
🙏🙏🙏🙏🙏🙏🙏

amirmahdi_s

Mine best teacher I often clearly satisfied by his work

aarifhussain

Exponentially better explained than school, I'm relieved

sxydutchmn

I solved this beforehand then went online looking for the solution. I’m surprised I got the right answer the first time lol, awesome video, Faculty of Khan!

ozzyfromspace

Life be really indebted to you for this lecture. Yes, I literally mean it❤️

hpavankumarmanti

Mate u need to do more videos you're very helpful.

darren

Amazing explanation... watching here in 2024. Thank you.

MosesPatsonPhiri

Side note in the end for the a_n you can just use fourier coefficient to find a_n it is easier computation.

mr.logzoid

It would be awesome if you could make some follow up videos on how to solve separation of variables for two and three dimensional problems. Thanks for great vids!

lucaswennerholm

How did you get am(L/2) on the RHS at 10:00 ? It looks so simple but i cant get that myself when I run something similar through an integral calculator

vernonroche

why does the value of n in lamda n can not be negative?

chaoma

Can someone explain why case 1 and case 3 are solved with different trig functions?

pianoguy

Hmm, it's not as hard as I thought it would be...genius idea was that the functions when divided are equal and if they're not dependent, they must equal a constant!

jibran

very useful vid helped me realise i’m utterly fucked

Jaffa-ytgx

The coefficient a_n contains O(x) and the function O(x) contains a_n, seems wrong to me, it is a paradox.

ryanmckenna

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