2025-10-05

[public] 177K views, 12.0K likes, dislikes audio only

3Blue1Brown

How dynamics explain Euler's formula, and vice versa.

Early view of the Laplace Transform video: https://www.patreon.com/posts/laplace-early-140428165

Instead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/support

An equally valuable form of support is to simply share the videos.

Home page: https://www.3blue1brown.com

Timestamps:

0:00 - Intro

1:51 - Euler's formula explained dynamically

9:27 - The harmonic oscillator

21:08 - General linear equations

22:47 - Motivating the Laplace Transform

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These animations are largely made using a custom Python library, manim. See the FAQ comments here:

https://3b1b.co/faq#manim

Music by Vincent Rubinetti.

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.

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Website: https://www.3blue1brown.com