@3blue1brown

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!

@smartereveryday

A modern mental masterpiece.

@matthyslaubscher8151

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

@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.

@kiwipaddy10

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

@MrBrightlight66

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!

@zulucharlie5244

100 years from now, people will watch this video and be thankful that you made it.  It's among the very best of what human beings and do with the internet and personal computer technology.  Thank you.

@saidelcielo4916

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

@Alex_1652

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

@flirkami

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

@Noah-rp7rv

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

@dainmeister

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

@Gabriele_Oliva

I'm Italian, and I haven't yet formally studied these topics, but your explanatory skills are incredible, you are able to discretize a complex problem in all its basic steps and then put it all back together.  I understood practically everything. I don't think I can solve a similar problem by myself, but it's a step forward, really thanks

@myrobotfish

Nothing more wholesome and satisfying than a 3Blue1Brown video

@ChrisAthanas

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

@rrrprogram8667

Oscars award for animation to be given to this channel

@RobertStander-xo2gu

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

@education4949

Omg !, he should be given the highest award in today's  world for explaining partial differential equations.

Respect and a salute