Derivatives center on the idea of change in an instant, but change happens across time while an instant consists of just one moment. How does that work? Brought to you by you: http://3b1b.co/eoc2-thanks Home page: https://www.3blue1brown.com/ And by Art of Problem Solving: https://aops.com/3blue1brown Note, to illustrate my point for the target audience of a new calculus student, I discussed a hypothetical speedometer that makes distance measurements over a very small time. Interestingly, most actual speedometers in modern cars work by analyzing the induced current of a spinning magnet, which is in some sense the universe implementing the derivative. ------------------ 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 about new videos, subscribe, and click the bell to receive notifications (if you're into that). ... https://www.youtube.com/watch?v=9vKqVkMQHKk

To mark 2^21 subscribers, in a style totally not stolen from Veritasium. Ties, shirts, etc. http://3b1b.co/store Links to things that came up below. The Bit Player https://thebitplayer.com/ The Idea Factory https://amazon.com/dp/0143122797 The Information, A History, A Theory, A Flood https://amazon.com/dp/1400096235 You can read about Lorenz in "Chaos", also by James Gleick https://amazon.com/dp/0143113453 Anthropocene reviewed https://www.wnycstudios.org/podcasts/anthropocene-reviewed Hardcore history https://www.dancarlin.com/ The Numberphile podcast https://www.numberphile.com/podcast Recent Quanta article on the eigenvector discovery https://www.quantamagazine.org/neutrinos-lead-to-unexpected-discovery-in-basic-math-20191113/ Channel supported by http://3b1b.co/thanks ------------------ Animations on this channel are largely made using manim, a scrappy open source python library. https://github.com/3b1b/manim If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a... Stream the music on Spotify: https://open.spotify.com/album/1dVyjw... If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ 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: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown... Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown ... https://www.youtube.com/watch?v=Agbh95KyWxY