Mastering Divergence & Curl: Visualizing Key Concepts in Maxwell’s Equations & Fluid Dynamics 🌊

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