General exponentials, Love, Schrödinger, and more.
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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 - General equation
20:03 - On 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
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https://github.com/3b1b/manim
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Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/
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