Visualizing two core operations in calculus. (Small error correction below) 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: 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 ------------------ 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, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com/ Twitter: https://twitter.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown