Chuỗi Fourier là gì? Từ dòng nhiệt đến vẽ bằng vòng tròn | DE4

Fourier series, from the heat equation epicycles.

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Special thanks to these supporters: http://3b1b.co/de4thanks

12 minutes of pure Fourier series animations: https://youtu.be/-qgreAUpPwM

Some viewers made apps that create circle animations for your own drawing. Check them out!

https://www.reddit.com/r/3Blue1Brown/comments/cvpdn7/make_your_own_fourier_circle_drawings/

https://isaacvr.github.io/coding/fourier_transform/

Thanks to Stuart@Biocinematics for the one-line sketch of Fourier via twitter. As it happens, he also has an educational YouTube channel:

https://www.youtube.com/channel/UCKOiJd9YCbv7LeL2LFOGiLQ

Small correction: at 9:33, all the exponents should have a pi^2 in them.

If you're looking for more Fourier Series content online, including code to play with to create this kind of animation yourself, check out these posts:

Mathologer

https://youtu.be/qS4H6PEcCCA

The Coding Train

https://youtu.be/Mm2eYfj0SgA

Jezmoon

http://www.jezzamon.com/fourier/index.html

For those of you into pure math looking to really dig into the analysis behind this topic, you might want to take a look at Stein Shakarchi's book "Fourier Analysis: An Introduction"

Timestamps:

0:00 - Drawing with circles

2:10 - The heat equation

6:25 - Interpreting infinite function sums

9:52 - Trig in the complex plane

14:11 - Summing complex exponentials

22:11 - Example: The step function

23:54 - Conclusion

Thanks to these viewers for their contributions to translations

Hebrew: Omer Tuchfeld

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These animations are largely made using a custom open-source python library, manim. See the FAQ comments here:

https://www.3blue1brown.com/faq#manim

https://github.com/3b1b/manim

https://github.com/ManimCommunity/manim/

You can find code for specific videos and projects here:

https://github.com/3b1b/videos/

Music by Vincent Rubinetti.

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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.

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