General exponentials, love, Schrödinger, and more.
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: https://3b1b.co/mat-exp-thanks

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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The Romeo-Juliet example is based on this essay by Steven Strogatz:
http://www.stevenstrogatz.com/essays/loves-me-loves-me-not-do-the-math

The book shown at the start is Vladimir Arnold's (excellent) textbook on ordinary differential equations.
https://amzn.to/3dtXSwj

Need a review of ordinary powers of e?
https://youtu.be/m2MIpDrF7Es

Or of linear algebra?
https://youtu.be/kYB8IZa5AuE

Timetable
0:00 - Definition
6:40 - Dynamics of love
13:17 - Linear systems
20:03 - General rotations
22:11 - Visualizing with flow

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Code for this video:
https://github.com/3b1b/videos/blob/master/_2021/matrix_exp.py

These animations made using a custom python library, manim. See the FAQ comments here:
https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim

You can find code for specific videos and projects here:
https://github.com/3b1b/videos/

Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/

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

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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

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