A free course offering the core concept of Calculus, with a visuals-first approach aimed at making you feel like you could have discovered the subject yourself.

Taylor polynomials are incredibly powerful for approximations, and Taylor series can give new ways to express functions.
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Full series: http://3b1b.co/calculus

Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced.
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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).

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OVERSEAS

Taylor series | Essence of calculus, chapter 11

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?
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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.

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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).

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The paradox of the derivative | Essence of calculus, chapter 2

A very quick primer on the second derivative, third derivative, etc.

Full playlist: http://3b1b.co/calculus


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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).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

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Higher order derivatives | Essence of calculus, chapter 10

A visual for derivatives which generalizes more nicely to topics beyond calculus.
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Essence of calculus series:
http://3b1b.co/calculus

Really nice applet made based on this video by Reddit user Larconneur:
https://www.geogebra.org/m/rftwacsy

Music by Vincent Rubinetti: 
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

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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

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The other way to visualize derivatives

Integrals are used to find the average of a continuous variable, and this can offer a perspective on why integrals and derivatives are inverses, distinct from the one shown in the last video.

Full series: http://3b1b.co/calculus

Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support

Special thanks to the following supporters: http://3b1b.co/eoc9-thanks

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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).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

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What does area have to do with slope? | Essence of calculus, chapter 9

A few derivative formulas, such as the power rule and the derivative of sine, demonstrated with geometric intuition.
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Great video by Think Twice showing this geometric view of the derivative of sin(x):
https://youtu.be/R4o7sraVMZg

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

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

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Derivative formulas through geometry | Essence of calculus, chapter 3

What might it feel like to invent calculus?
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In this first video of the series, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus.

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These animations 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:
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Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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.

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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).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

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The Essence of Calculus, Chapter 1

A visual explanation of what the chain rule and product rule are, and why they are true.
Full series: http://3b1b.co/calculus
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And by Brilliant: https://brilliant.org/3b1b

Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support

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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).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

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Visualizing the chain rule and product rule | Essence of calculus, chapter 4

Formal derivatives, the epsilon-delta definition, and why L'Hôpital's rule works.
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Full series: http://3b1b.co/calculus

Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support

------------------

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).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

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Limits, L'Hôpital's rule, and epsilon delta definitions | Essence of calculus, chapter 7

What is e?  And why are exponentials proportional to their own derivatives?
Full series: http://3b1b.co/calculus
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A mistake at 12:30: What's written as "(1   r)" should really just be r, by any usual convention for how to write an interest rate.

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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).

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What's so special about Euler's number e? | Essence of calculus, chapter 5

Implicit differentiation can feel weird, but what's going on makes much more sense once you view each side of the equation as a two-variable function, f(x, y).
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Full series: http://3b1b.co/calculus

Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support

------------------

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).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

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Implicit differentiation, what's going on here? | Essence of calculus, chapter 6

What is an integral?  How do you think about it?

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Full series: http://3b1b.co/calculus

Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support

Special thanks to the following patrons: http://3b1b.co/eoc8-thanks

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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).

If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended

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Essence of calculus