2018-06-21

[public] 2.37M views, 131K likes, 571 dislikes audio only

3Blue1Brown

Visualizing two core operations in calculus. (Small error correction below)

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

My work on this topic at Khan Academy: https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives

Timestamps

0:00 - Vector fields

2:15 - What is divergence

4:31 - What is curl

5:47 - Maxwell's equations

7:36 - Dynamic systems

10:37 - Explaining the notation

13:28 - No more sponsor messages

Correction at 4:55, the narration should say "counterclockwise rotation gives positive curl, clockwise rotation gives negative curl". The diagram is correct, though.

For more fun fluid-flow illustrations, which heavily influenced how I animated this video, I think you'll really enjoy this site:

https://anvaka.github.io/fieldplay/

Music by Vincent Rubinetti:

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

Thanks to these viewers for their contributions to translations

Hebrew: Omer Tuchfeld

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