
Solving the heat equation: Differential equations, chapter 3 [video] - espeed
https://www.youtube.com/watch?v=ToIXSwZ1pJU
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shoo
For an odd application of PDE: you can define and solve boundary value
problems over spatial domains in games to find a solution over the playing
field that measures how near or far you are from desireable or undesireable
locations. Then objects in the game (e.g. actors controlled by AI) can use
simple gradient ascent / gradient descent using the local gradient of the
solution to determine how to move, in order to e.g. avoid threats or chase the
player

[https://sgd.cs.colorado.edu/wiki/Collaborative_Diffusion](https://sgd.cs.colorado.edu/wiki/Collaborative_Diffusion)

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antisemiotic
Poisson's Equation is also used for mesh reconstruction:
[https://en.m.wikipedia.org/wiki/Poisson%27s_equation#Surface...](https://en.m.wikipedia.org/wiki/Poisson%27s_equation#Surface_reconstruction)

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vmurthy
I recently read a book on the life of Faraday and Maxwell[1]. Very
interestingly, Maxwell modelled the famous equations of Electromagnetism by
imagining them to be similar to how _heat flows_. To me that is a great take-
away: Trying to model a phenomenon based on an existing phenomenon (within
reason, of course) and changing the world with it!

[1][https://www.goodreads.com/book/show/18240286-faraday-
maxwell...](https://www.goodreads.com/book/show/18240286-faraday-maxwell-and-
the-electromagnetic-field)

Edit: some formatting

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DavidSJ
I read this book too and can also recommend it.

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kmill
Here's a small toy to play with the heat equation:
[https://math.berkeley.edu/~kmill/toys/heat/heat.html](https://math.berkeley.edu/~kmill/toys/heat/heat.html)
(it probably doesn't work on mobile---sorry!)

It shows the Fourier transform of the curve you draw, and how each summand
decays through time.

There's also a wave equation toy:
[https://math.berkeley.edu/~kmill/toys/wave/wave.html](https://math.berkeley.edu/~kmill/toys/wave/wave.html)

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bschne
3B1B is one of those content creators that consistently puts me in awe at how
much stuff is out there today that is both very informative _and_ very well
produced.

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enriquto
I love the subjects they treat and the teaching style; however, a video is
useless to me, i can't follow an argument in video format for some reason. If
there were textual transcripts of the same words with static illustrations (or
a few, non-automatic animations) it would be much more useful.

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nayuki
It sounds like what you're asking for is a paper textbook.

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enriquto
It can be a website also. Animations are cool, as long as they are not
overwhelming.

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DigitalTerminal
I'm not sure what it is about this video I don't like. It just didn't seem
very much like a 3B1B video for some reason. Maybe it's because there were
fewer "A HA" moments than in other videos. Maybe its the source material. Just
feels...different.

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mmq
Not sure why you did not have any "Aha" moment, bu the visual explanation used
for the principle of superposition and approximation of functions by Fourier
series is very informative. I also liked the explanation about the
proportional relation between temperature and space in the heat equation. I
think in most higher educational systems, they only approach this type of
problems with pure theoretical solutions/explanations.

