3Blue1Brown - 2019-06-16
Boundary conditions, and setup for how Fourier series are useful. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/de3thanks More about the heat equation, with a derivation in terms of slope corresponding to heat flow from MIT OCW: https://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-fall-2006/lecture-notes/heateqni.pdf If you want to learn more about Fourier series, here are a few great videos/posts which I think you'll enjoy: Mathologer's: https://youtu.be/qS4H6PEcCCA The Coding Train: https://youtu.be/Mm2eYfj0SgA Jez Swanson: http://www.jezzamon.com/fourier/ ------------------ These animations are largely 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 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: 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
“This makes for a good stopping point.”
No, no it doesn’t 😢
Group hug sniffles
@justcarcrazy NAO, the word is NAO.
666 likes with 6 answers
@GDash 69 You ruined the 6 responses with your seventh comment... and now I made it worse with an eighth!
:(
you know this is the best educational channel on YouTube when your maths professor recommends it.
@張海鷗 If you're going to try to scare me or somehow make believe what your comment says. At least type it in English.
my physics teacher told me about this channel when he found out about my addiction to learning stuff which is out of the syllabus lmao
@張海鷗 exactly! 😁
Both essence of linear algebra and essence of calculus are recommended material by my professors.
Both your professor and 3blue1brown are MVPs. I wish they never stop do the knowledge.
And this is all for modeling a one dimensional Bar...
One dimension, with different temperatures on each point. There you have a function which makes 2 dimensions. Then you can always add time. See, you had 3 dimentions from the start
FEM solves this for breakfast
I was trying to pick a research topic for my Bio paper. I was trying to go in the genes and ecology realm, specifically about bees...
I started to research it a little more and you would not believe the differential equations I would have to do. I love math and didn't mind doing integrals but when I saw 16 pages of complex differential equations I almost cried. No, no thank you.
@Zeyda Lynn wow. How come it's that many? Is it all related to genetics?
@張海鷗 Was soll das denn?????
I'm genuinely waiting for the Laplace Transform one.
That will be a glorious, much anticipated/requested day. I predict it will happen three videos from this one
Really in need of that one, god of math hear my pray and provide us with your knowledge
I thought he did but it was the Fourier Transform..
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
one could almost say we were Granted access to this video
(\____/)
( ͡ ͡° ͜ ʖ ͡ ͡°)
\╭☞ \╭☞
It is amazing
My friends : what kind of series do you watch?
Me : that's kind of complicated..
no it's not
yeah, you have finite friends
You have the sexiest math lessons, ever!
So smooth, so luxurious...I bet your animations even smell good.
This is such a hilarious comment!
i think you mean maths lessons, all the fancy people say maths
@Erick Yip Pon INDEED!
I concur especially since I am a very fancy person.
I literally yelled "No!" when you said you were splitting Fourier into its own video. This stuff is so good, I want to see all the things right now! 😥
I know what you mean but the material would be less good (less calmly explained, maybe a few errors, less intricate animations and simulations) if he rushed it. So I'm happy to wait :)
He already has videos on Fourier transforms and series, jsyk
@Anselm David Schüler Yeah, I know. But none of them covered this area of application, afaik. And I was finding this example really helpful.
top 10 cliff hanger endings off all time
"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.
This, for me, is the key of why math is invented and not discovered
True math geek.
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I'll design one, hold my beer :D
Engineers don't always get things right, they get things right enough.
This is the point of my life, where I realize how idle have I been :( I have a PhD. in Maths and don't understand what he said about the flat thing in the boundaries (I could solve the equations as a student, yeah, but didn't understand the meaning); I will watch the video again... be dilligent and start again if necesary :( Thanks a lot for the very illustrative videos
Actually, it could sound wierd, but math experts usually dont even have to undersand the physical meaning of PDEs and similar stuff. They have strong formal logical reasoning and use is to solve problems. Thats what physicists are for :)
could you not have posted this series before my exam :D
same haha
Lolol this was me after finding his calculus series and realizing it posted a year after I had already finished high school 😭.
My semester final results are also out!
😄😄😄
I actually got excited seeing this in my subscription box!
i nearly shit my pants!
SAME
0:26 "where there's curvature in space, there's change in time" can you or someone please explain it a bit more
By all means, take a look at the previous video :)
Oh the gods truly blessed us today. My goodness. How long have I been waiting for this. Thanks you as always.
E X A C T L Y.
for the first time in my life I feel like the little Topology I learned through Calc 2 is finally making sense and when you said I should be happy if I understood what was happening I had the biggest shit eating grin of my life
The series means a lot to me. Thank you for making these brilliant videos.
3:57 Can you explain why, after some tiny timestep, everything scales down by a factor?
Because the rate of change for each point is proportional to the size of that point. So for example, if the rate of change was -2 * the magnitude at each point, then after a time step of 0.01, each value T would shift to about - 2 * T * 0.01, so it would move to T - 2 * T * 0.01 which is (0.98) * T. Since this constant is the same at all points, the whole function T shift to 0.98 * T. That's if the time step was 0.01, but you can also think about what happens as this time step tends towards 0.
@3Blue1Brown but this is true only when second derivate with respect to time is zero, right. Are we assuming it to be zero, I am not sure here.
@kumar shivang The rate of change of each point is proportional to the size of the point just before the current time step, not at t=0. So, the second derivative won't be 0 - if it was, then the graph at 5:50 would be a straight line and not curved.
@Keeran Parthipan exactly, then scaling bit doesn’t make sense, since by initial conditions we only know at t=0 time rate at any point to be zero it doesn’t rules out the possibility of second rate of time.. which means at any other instance there could be non zero time rate, then scaling deduction is wrong.
Im about to take DE in 2 months man I wish this series could finish sooner. Thank you for the legendary content btw!
Just Learned how to solve this Stumm-Liouville tipe of equation on my post-graduation
Omg I just realized there’s 3 blue pi’s and 1 brown one 😭
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
Ooh new video
Rip my sleep again
Shit here we go again
Ahhhh, but it's worth it.
3.21 - I'm one of the night viewers, too.
But instead of watching it on uneducated videos, you watch it here. Good job
提交參政言論活動中破壞性者侵入行竊侵竊違規職務罪嫌移送移除頻道革職法辦處理。需求借貸金融界銀行業集團旗下品牌形象廣告協議約定隱私條款及服務滅族性系統工程殘害損譽資金賠償刑責責任依法共同體分擔摧毀公共建設性重挫影響下理賠金額巨額虧損資源產物保險公司危機處理
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 .
You do a really great job of explaining. I understand things now that I never knew, plus a lot of things I thought I knew but was totally wrong... Much appreciated.
Those Boundary cond. are also called: Neumann boundary condition. Other examples of Boundaries are Dirichlet or even mixed boundaries :).
Love these to death. Half my life I've seen ALL the trees in a forest. WTF!
Thank you so much for these series! They've helped through a lot of useful maths. You've been an inspiration! My roommate and I actually started this channel recently with hopes to make the same kind of insightful content. We just launched a new video (on whether there is more sand on beaches or stars in the sky) and would love if any of you'd like to check it out!
Please, please, please don't make us wait 8 more weeks. That was hell.
This video feal so quickly and natural, that it feel like a time jump into the future.
Wow, those three dimensions curved surfaces representations are precious
Completely blew my mind when you were talking about using sine waves for an function and I realised it: the graph’s second derivative will be the reflection of the the graph in the x-axis 🤯
This is so rich with content that I find myself pausing every few seconds just to appreciate the imagery and your artistic approach. Simply Beautiful.
Yo bob, you reading the right book?
@New Kid , not sure what you mean.
Bob Tivnan It’s okay man...
所有參政言論活動中破壞性者提交違規行為摧毀性系統工程滅族性操作方式執政者，都必要革職移除頻道，終身不得登入帳號密碼遊戲經商使用，移送法辦監獄服刑處分
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.
This applies to vibrating string as well? I remember hearing about this from a classmate but haven't taken PDE's yet
Even tough I know this stuff, it's still mesmerizing watching the demonstrations
Amazing! Incredible work. Maths is amazing and you sir have made it accessible to everyone, as it should be. Thank you! I have learned a lot! I wish I could be able to develop these simulations for my classes as well. I love all your videos!
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.
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.
You have an amazing gift to explain visually as well as through your narration the abstractions of higher level mathematics. If I only had your excellent videos when I was in graduate engineering school.
Wish I had such clear explanations at university
I was just thinking about 3B&B video.
Thanks
A mind-blowing clarity!
I think it might be difficult to thank you enough for your contribution in spreading the love of (mathematical) beauty. I really agree beauty is the language of the universe.
I've waited really long for this one.
I've been waiting for this video for a month! Love 3Blue1Brown!
tmr is my Physics exam
Good luck my dude
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.
Sir, I genuinely thanks you from the bottom of my heart. I, despite being in medical profession, try to learn math for joy, in my leisure time. your videos help a lot.
Your animations get more ellegant with each new video you make!
Hmm, so it seems that cosine functions (with zero derivative at boundary) makes sense for unbounded rods, where the rods are not subject to any temperature constraint. What would happen if we set the temperature of the rod at some constant temperature?
3Blue1Brown - 2019-06-16
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!
Steven Vargas - 2019-07-16
More like twisted wave length
Steven Vargas - 2019-07-16
Heat is just how use of fuel we use to make something
Steven Vargas - 2019-07-23
@Staben it okay I'm sorry I'm just a show off I gusse
Steven Vargas - 2019-07-23
@Stefan Kaiser it okay I sometimes a show off I need relax with this thing
Giacomo Mastroddi - 2020-11-16
are you going to upload new videos in this playlist?