3Blue1Brown - 2019-04-21
The heat equation, as an introductory PDE. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/de2thanks Infinite powers, by Steven Strogatz: https://amzn.to/3bcnyw0 Typo corrections: - At 1:33, it should be “Black-Scholes” - At 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. ------------------ Animations made using manim, a scrappy open source python library. https://github.com/3b1b/manim 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: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u 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. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown
I can not give enough praise on the quality of animation coupled with the explanation. Amazing - Thank you
Same here.
yes, its amazing!
Aniplation
My teachers at university are morons.
2:23
Mathemations: function
Linguists: letter
Musicians: forte
Gamers: respect
press 𝒇(x) to pay respect
@AnteConfig you know what BIG PPS do????? Thats right they play Tuber Simulator.
Pewds: PP
Violinist: f-hole
Stewart: Calculus
@Arvid Johansson ?
"Baby Face Fourier" sounds like a gangster.
Fourier The Baby Face 😂
"Baby-faced, poodle-haired Fourier"
DI MOLTO
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.
Malthe Wellendorf Gissel i studied electrical and we also need to be comprehensive in PDE
I'm in research physics, and this is a helpful starter
Same boat. But I do find it interesting that I am able to follow this video without even stopping and thinking about it as I got so used to not being able to visualize anything in math anymore. I am just like "ohh see, you can imagine it this way". So my university in a way did a great job
This is so great, I finally understand this concept after 32 years
wait what
If ANYONE had explained the Laplacian as the relationship of the value of a point to the average value of its neighbors to me during my fluids class, my grade could have been a full letter higher.
I've just learned this concept today!!! 😭
Yeah what the hell. I always knew second derivatives represent curvature in some way but the way the second difference was directly connected to the Laplacian was amazing!
I’ve done the multivariable calculus lessons you recorded on Khan Academy and I gotta say, I’m getting flashbacks
@Noah Thank you so very much for posting this link. I suppose I could have found it, but I appreciate it because it leaves me no excuse not to watch them.
i didnt realize that it was him 😓
im in the middle of it
Great video! Btw, Fourier is pronounced as "foo-Ree-ay".
@3rik R Vargas Partial and derivative?
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
Uhm, where you have been in the 80ies, when we had to learn this the hard way? :)
I have the same damn question. Those days without internet, you tube and this class of videos for free to watch?
I never though I would ever binge watch math in this lifetime.....
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!
3:46 he started at π, went to e^2, then to phi, and ended at tau.
3:45 i love how x goes from pi to e^2 to phi. Amazing little easter egg.
Edit: what the heck likes
I can't see anything...
You could say it goes from pie 2 phi
Don't forget about 3:46! =)
@Atin Bainada it's tau.
π -> e² -> φ -> τ
3:37 : What the F...unction
but seriously, thanks for this amazing work!
Haha I also observed it🤣🤣
I like the little easter egg at 3:49 of 7.389 for e², 1.618 as the golden ratio at 3:54 and the controversial pi or the double of 3.14 when you were showing a change in your graph at 4:00
While watching this video, I was considering how you do your animations. I am a huge fan, and stumbled across this series as part of my quest to watch all of your content. I have noticed you have a pretty consistent animation for drawing straight lines - that is, the accelerations are pretty constant and look the same, have the same energy when looked at, etc etc
But then I got to thinking: how in the world would someone define that line-drawing behavior? Should it draw at a fixed velocity, always drawing the same proportion of the line with each time step? Should it accelerate and then decelerate, like the one you use? Maybe it should start moving quickly, but end slowly? I have no idea! I don’t think anyone could just pop into whatever animation software, draw a nice velocity curve, and say “yes, this is what I want because I have solved the problem of animating lines.” Humans can’t pull that arbitrarily out of a hat, and math doesn’t have those answers.
But then I realized, if you look at an example animation - well, everything changes. That animation is way too slow; I think it would look better faster. Going at a constant rate is boring, add some energy with dynamic speeds.
Humans cannot just generate numbers like that and expect them to work. But what they can do is look at a preexisting condition and say if it’s too high or too low, if it’s too fast or too slow - indeed, we are differential equations generators ourselves!
Thanks for helping me see math in yet another area of our lives
This is probably one of the most beautiful, satisfying videos I've ever ever seen in my lifetime. I sometimes have the wish of making YouTube videos on math or physics in my language (br portuguese), but every time I come visit this channel I feel like I'm far from ready. Thank you Sir!
Normies: waiting for game of thrones
Big PPs: waiting for 3blue1brown videos
Rommel Albay medium PP
@Rommel Albay pp undecided
What is Big PP?
I don't watch any game of thrones so I guess that makes me one of those Big PP types, but I'm curious... are you trying to say I have a big PP or...?
@Rahul Sahi yeah it's cool
The worst grade I ever received in my academic life was in PDE.
Man I wish we had this quality of exposition for cutting edge research papers
Me too
This channel is one of a kind. At least two or three cuts above all others attempting to illuminate math. BRAVO!
Mathematics is a very beautiful language, and most certainly misunderstood by most people and frightened by its complexity (myself included). I love how you make them alive and you just made me genuinely interested in Math. I will revise my old University notes on differential equations (something that haunted me for years) and try to look at them from a different perspective. Thank you for inspiring thousands of people like me to better understand Math.
Those graphics are really getting exceptionally good! The 2d representation animation at 4:13, for example, is just gorgeous.
yeah seeing the solution in both time and space is nice. it especially demonstrates the different behavior of it in the different dimensions well. the Fourier series in space and the exponential decay in time.
also, woooo 413
@Timestoppa thanks so much!!
God*
I remember my struggle in university with that steady-state and transient analysis. This one simple animation (not so simple in the back-end though ) 4:13 could have saved me hours and days. Grant Sanderson is going to revolutionize Math communication.
I paused the video at 4:22 to write a comment about how great this particular viz is. I mean, it's just so elegant.
13:41 how did you get the equations of their respective accelerations, sir? The units of acceleration (L.H.S) doesn't match with the R.H.S .
This video was just downright awesome! I used to be intimidated by partial derivatives, but the graphs and animations helped me understand that they are quite simple. Great job 3b1b.
Never thought I could "come up with" the heat equation, until you said so.
Finally. I've been wondering about this stuff.
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.
I feel you on that!
preach it bro..
I definitely agree
This is why a good teacher is so extremely important. Bad teachers present the subject matter, and the students are obligated to practice is, and start to dislike it. Good teachers explain with passion what their subject matter is used for, why it is done this way, and how amazing it is to capture something complex in such a simple way, and the students become intrigued and start to share in the teacher's passion.
The key of maths which seems so abstract is the basic explanation in a simple way of introduction
1) WHAT
2)WHY
3)HOW
Most of the teachers, professors are busy with the HOW question without explaining the basics WHAT and WHY... so they miss the target...
In this exemple the expkanation starts with WHAT and WHY... which are the foundations. The HOW doesn't allow you to UNDERSTAND but only to RESOLVE the problem...
Without understanding it!
The WHAT-WHY-HOW must be given by a MENTOR with simple words ... which is the case in this exemple.
Welcome in the world of sciences abd maths...
I like how at 3:46, the notch goes from π to e^2 to ϕ to τ. Nice touch, and great video as always!
Would that we had these gorgeous animations when I was in high school and a cell in a Biology textbook was a puddle with cylinders and a a blob inside (It’s more like a city) and atoms were mini solar systems (If an atom were the size of the Sistine Chapel with the altar as its nucleus the electron - more like a wave -would be a butterfly fluttering at the ceiling).
Ten of these PDEs comprise Einstein’s General Theory of Relativity (His space time theory of gravity, not Special Relativity which is E=mc2), and you can see why they would be as per the speaker here explaining the axes of space and time.
You just outdid yourself... once again! How is that possible?
Thanks!
Omg !, he should be given the highest award in today's world for explaining partial differential equations.
Respect and a salute
Grant, I believe that you have THE BEST channel on YouTube (regardless of topic). As others have pointed out, it's getting better and better in terms of technical polish, graphics etc. Thanks so much - I hope you are loving the work! I predict that your channel will go down in history as being on par with the most well regarded Math Textbooks ever written. Let's not forget that you are also one of the pioneers in this new media. Keep going!!
I just need to watch one of your videos, and suddenly, I there was anything that I was confused about, it immediately becomes clear to me!
11:34
Isn’t the eq suppose to be (dT2/dt)=c*delta*delta*T2 ?
Good question.
It doesn't matter, it's still a constant
The best teacher i ever had... now i know what mathematics really is
The essence of mathematics is not to make simple things complicated, but to make complicated things simple 🕊️
@Philippe LePilote Great, as if my calculus wasn't hard enough now it's levitating and demanding sacrifices.
@Mind Math Money The first one
@Spot But is math, *real*?
Vsauce music plays
@Slangens ; I respectfully ask you to be careful here, because the fact it doesn't descibe anything in our visible world, doesn't necessarily mean there aren't dimensions of the universe where those solutions describe something or that there isn't a paraelell universe where the math even more wonderfully applies!
@How mathematicians create maths I'll be short here - It seems like your definition of "universal language" is a bit off from the usual one. I refer by that to something that describes the world 'we' live in. Have a good day.
The effort, intuition and love that goes behind these videos is so real and well thought and the eloquence that comes out is satisfying. It’s about time that education is revamped as rigorously and intuitively as in 3B1B... 💕
11:00 - Should be "ΔΔT2"?
I am also stuck at this point, seems it should be with respect to T2
Why couldn't you have made these a year ago when I was struggling through partial differentials in math class?
But what is a partial differential equation?
Ans - It is something I've been waiting for you to make a video on.
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!
when will the next vid be up?
Are you okay? I'm starting to worry.
I would love to watch a combinatorics or number theory video series
Good day! Could you please tell what software you use to produce these animations? I admire them greatly and I would like to learn how to do something similar as supporting material for my seminars. It has probably been asked many times before, but I couldn't readily find your answer in the comments. Thank you!
Can you do Avideo about Fuzzy Logic , Sate Space,
I'm gonna show this to my calculus professor. That'll show him.
This explanation is better than my the explanation of my prof in a complete semester of pdg. Great job
As a nuclear engineering student, these equations always show up and everyone just runs away from it, but watching your videos make them less intimidating. For example, nabla operator is just a short form of the partial derivatives wrt xyz. I honestly was terrified of this symbol for so long haha
This is truly the most elegant explanation of a PDE I have ever seen. Your ability to make seemingly complex math so visually intuitive is a gift and I am just grateful to be able to experience it. Never give up on this talent and passion of yours
This is Awesome !!!, Youtube recommended this video and I couldn't stop watching although I had to rush to another commitment. Darn, I better get going or Im going to be late. I will come back and watch all your videos next. God Bless, This is a great video cant recommend enough !!!!
I like how you use finite difference method to describe and derive the heat equation. 👏👏👏
SmarterEveryDay - 2019-04-26
A modern mental masterpiece.
Vishank - 2020-07-01
Yepp it is truly beautiful! Also, it is a delight to see you here sir! Please keep up the good work😄💎
N Satheesan - 2020-08-14
How does this have so few likes?
Convilious - 2020-09-04
why only 3 replies?