Solving the heat equation | DE3

Boundary conditions, and set up for how Fourier series are useful.
An equally valuable form of support is to simply share some of the videos.

More about the heat equation, with a derivation in terms of slope corresponding to heat flow from MIT OCW:

If you want to learn more about Fourier series, here are a few great videos/posts which I think you'll enjoy:

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
Download the music on Bandcamp:

Stream the music on Spotify:

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

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Various social media stuffs:

[bluebrown]

Next up we _finally_ get to Fourier series, which will be the beginning of a turn in the series towards understanding the surprising depth and importance of exponential functions for differential equations. Stay tuned!

[chriskindler]

you know this is the best educational channel on YouTube when your maths professor recommends it.

[pearceburns]

"Seek Idealized problems ->[Find] General solutions -> [Create] Realistic models" ( 3:20 ) resonates with me, and I would definitely love a poster with this mantra on it.

[jibraniqbal]

This took a while but I know I'm going to enjoy it so the wait is most definitely worth it. Thanks for the content, Grant

[aniksamiurrahman]

To a math noob 3Blue1Brown videos are like heavenly inspiration. Intuition conveyed here often acts like the light at the end of the frustrating and treacherous tunnel. But as the course advances more and more things starts to make sense and the video wears well as one grows more experienced.

[diaz]

I'm genuinely waiting for the Laplace Transform one.

[gonzalezm]

“This makes for a good stopping point.”

No, no it doesn’t 😢

[TebiByyte]

I'd like to point out that this is something that is done in Quantum Mechanics quite a lot! Being able to exploit the linearity of a PDE, and then finding solutions using a Fourier Transform is immensely powerful. In my opinion, it's some of the most beautiful mathematics that I've ever come across.

[YourThermalWorld]

I graduated BSME in 1978. ODE’s and PDE’s actually made sense to somewhat but I didn’t fully understand them. Now that I am retired, your channel has enriched my knowledge immensely. I thank you for stimulating this Senior Citizen’s mind!

[Mayank-mfxr]

in first semester, i had calculus and you had your series on it going on . awesome .

i had linear algebra in 2nd semester and oh god you had a series just then . awesomely awesome .

and now . i will be starting course on differential equations for my 3rd semester . and guess what ... a golden series on DEs is going on .

this is not fake and is a very very good motivation for me .

[AaronFresh]

You should know how important this channel and the videos you make are to the online learning community. Nothing else, not even your early work at Kahn academy, comes close to how comprehensive and professional the videos on this channel are. It is an invaluable source for self learners and I hope to see many many more.

[tehnbpwnr]

Grant, your last video inspired me to go away and knock a spreadsheet numerical solution together for the 1D heat equation and hence gave me a much better understanding of what's going on. It's what made me realise that a linear function is a solution to the equation when I was placing around. Please keep this going.

[FF-wloo]

Hey Mister, I just wanted to let you know how grateful I and probably many many others are for these kind of videos including the visualization. You know, sometimes when you are learning some new things, it can be very hard to imagine something just out of a line in a book or article. I can imagine these videos take hell of a time to make, but they are superb. I often times spent even days thinking about only a few pages in a book trying to understand something I read, meanwhile googling for all sorts of videos, until I made my mind clear and this is a perfect shortcut to understand. Here goes my thanks as well as thanks of many other students and possibly many other people who love maths.

[AaronPM]

I started watching your videos in high school and I'm currently doing signal processing and modeling at my current internship where I look at PDEs all day and I still find every video you make extremely enlightening. Thank you.

[stevestarcke]

In Chemical Engineering, heat transfer is extremely important. For the first time I understand where these thermodynamic equasions come from. The world is even more beautiful than I thought. Thank you for the insight!

[DiracComb.]

Given that I’ll have to take this course in my college curriculum, I appreciate the well done and extremely insightful resource. Pls don’t cancel the series

[toebs_]

I watched through your videos on linear algebra a while ago and thought to myself "man, if only I had seen these while taking my linear algebra course, it would have given me a lot more intuition for the subject a lot easier" and now this, in the middle of my course on integral transforms and differential equations :D
Thanks a lot, you're doing a great job.

[pptqjsl]

The series means a lot to me. Thank you for making these brilliant videos.

[lucasnicoara]

I actually got excited seeing this in my subscription box!

[owensilberg]

I watched this a while back without having any real knowledge of differential equations, and now that I'm a decent fraction of a semester into dealing with them it's awesome to see this video again having dealt with the tools that're mentioned!