But what is a partial differential equation? | DE2

The heat equation, as an introductory PDE.
An equally valuable form of support is to simply share some of the videos.

Timestamps:
0:00 - Introduction
3:29 - Partial derivatives
6:52 - Building the heat equation
13:18 - ODEs vs PDEs
14:29 - The laplacian
16:04 - Book recommendation

Typo corrections:
- 1:33 - it should be “Black-Scholes”
- 16:21 - it should read "scratch an itch".
If anyone asks, I purposefully leave at least one typo in each video, like a Navajo rug with a deliberate imperfection as an artistic statement about the nature of life ;)

And to continue my unabashed Strogatz fanboyism, I should also mention that his textbook on nonlinear dynamics and chaos was also a meaningful motivator to do this series, as you'll hopefully see with the topics we build to.

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 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:

[matthyslaubscher]

I can not give enough praise on the quality of animation coupled with the explanation. Amazing - Thank you

[bluebrown]

Next up, we'll look at how to solve this with Fourier series, including some discussion of boundary conditions. Stay tuned!

Edit: I see a number of questions about changes at the boundary, so maybe I’ll add a quick note. For example, some of you ask if a function with constant non-zero slope is stable. Indeed, this is something that needs to be specified for a well-defined solution, so good question! The heat equation as described here only describes the interior. The easiest boundary condition to work with is when each endpoint is held fixed, e.g. if the ends of the rod were somehow constrained not to change temperature. In that case, straight lines are a stable solution. But other conditions can be specified too, as you’ll see!

[MrMaltheWG]

I have studied mechanical engineering for almost 5 years now, and this is the best explanation of PDE´s and fourie series I have ever heard. Thank you very much for fantastic illustrations and intuitive explanations.

[kiwipaddy]

3B1B deserves a Nobel Prize for explaining math! Simply outstanding, yet again.

[debblez]

3:45 i love how x goes from pi to e^2 to phi. Amazing little easter egg.

Edit: what the heck likes

[Noah-rprv]

I’ve done the multivariable calculus lessons you recorded on Khan Academy and I gotta say, I’m getting flashbacks

[flirkami]

Those graphics are really getting exceptionally good! The 2d representation animation at 4:13, for example, is just gorgeous.

[dainmeister]

2:23
Mathematicians: function
Linguists: letter
Musicians: forte
Gamers: respect

[saidelcielo]

I've watched countless 3B1B videos and they're all illuminating and high-quality. This one, among those, is an absolute masterpiece.

[MindMathMoney]

*The essence of mathematics is not to make simple things complicated, but to make complicated things simple* 🕊️

[Alex_]

This channel made me realized that I don't actually hate math.

[vg]

pleasantly surprised to see 3k views in 10 minutes on a math video

[Brynmawrhill]

5:30-6:15 Got it! Partial differential equations aren't actually partial. They are complete - but only as a description of part of the system. Thanks!

[olehborys]

Just want to thank you for what you do for me and milions of other students, trying to understand such a difficult (but very intuitive after your videos) area of math. Your explanation if very clear, animation is outstanding. I really hope you will continue doing videos this way.

[MrBrightlight]

I used to hate maths in a very profound manner. The reason was that it was presented in a manner like a recipe...do this that and the other in such and such a way and good food comes out. There was no understanding of what was going on and this was most frustrating. The internet, through people like 3 blue 1 brown, helped to propel me to the opposite side of the fence. Although I am no mathematician, I can now appreciate and admire the beauty and power of mathematics. There was clearly a lot of work behind this video to illustrate a complicated subject relatively easily. I wished I had access to such a tool when I was much younger.

It would greatly help the younger generation to give them access to material such as this and to encourage them not to shy away from maths. As with most things beautiful, their creation is not easy but nothing to be terrified of either.

[KraylusGames]

I'm a computer science grad and I've taken a handful of classes which required the use of ODEs and PDEs. After watching this video, I feel like I have finally gained a full conceptual understanding of how they fit into the larger scheme of operations in math and cs. The visualizations you created were absolutely incredible, but the explanation was perfect. Thank you so much!

[CStrikr]

Me: "I'll just watch the first 5 minutes to see what it's about and get back to work"
*watches the whole 17 minutes*

[faresabbasi]

3:37 : What the F...unction


but seriously, thanks for this amazing work!

[codersgarage]

And, I just actually think that this is the best channel to gain rock solid intuition in math. Thank you ☺️

[ChrisAthanas]

This is so great, I finally understand this concept after 32 years