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

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  @3blue1brown · 9 years ago (edited) · pinned

  The next and final (for now) chapter of the series will be on Taylor series, with a small footnote on higher order derivatives coming along with it. &nbsp;Follow the full playlist at <a href="https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr">https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr</a>

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  @dabeer1991 · 6 years ago

  i have fallen in love with maths again. I teach physics and as an educator, i have genuine respect for your creativity and lucidity. BRAVO!

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  @rishavdhariwal4782 · 2 years ago

  &quot;when you reframe the question of finding an average of a continuous value as instead finding the average slope of a bunch of tangent lines it lets you see the answer just by comparing endpoints.&quot; This was the highlight for me in this video

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  @FacultyofKhan · 9 years ago

  Who needs Saturday-night nightclub escapades when you have 3blue1brown&apos;s videos to keep you entertained?

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• FR

  @franzluggin398 · 9 years ago

  Those pi-creatures are a subtle, but at least for me very effective way to make the parts of the video that are non-visual have more of an impact. They do so many things, emoting how you think the audience feels at the moment (and asking questions when you want to tackle them), tracking what&apos;s going on on the screen with their eyes, pointing at stuff, ...<br><br>This alone must have been so much work! You also made their various poses very expressive, and not to forget cute.<br><br>I&apos;m not really going anywhere with this other than a big &quot;Thank you!&quot;. It&apos;s so rare so see something of such consistently high quality, much less for free!

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• LO

  @louisng114 · 9 years ago

  I think about the average of a continuous variable as shaking up a bucket of sand until it levels. Since the amount of sand is constant, the area under the curve stays the same. New shape is a rectangle with the area being the base (interval length) times the height (average value). Therefore, the average is the integral divided by the interval length. This can be extended to multiple variables.

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• MR

  @MrBebopbob · 9 years ago

  Absolutely beautiful. &nbsp;I showed this to my teenager that just finished college calculus and he was blown away at the intuition it gave him. &nbsp;We need to clone you, and replace all the uninspiring math teachers in this country so kids will understand the amazing beauty of mathematics. Thanks for the hard work. Bob

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  @Psi2610 · 9 years ago

  I&apos;m in s1 (12 years old) &nbsp;and don&apos;t understand any of this but I still think all your videos are amazing

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  @ThePatientPianist · 9 years ago

  No kidding, you are an absolute inspiration for me (I&apos;m planning on becoming a high school teacher). <br>This is math taught the way it should.

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• LC

  @lcarsos · 6 years ago

  At some point I understood math&apos;s symbology, and got good at moving around all the variables and bits of notation. This meant that I could answer homework questions, and do most test problems, but I had no intuition for what was happening. It took me many years (and failing classes a few times when I ran into a professor that cared more about understanding than good test takers) to build up an understanding for what was happening when I was shuffling all those bits around on the paper.<br><br>Thanks for your really excellent videos.

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  @ultravidz · 9 years ago

  Hey man if you ever stop making videos ima track you down

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  @SamuelAndradeGTutos · 9 years ago

  You are actually the best professor i ever had. <b>-</b><br><br>Tks from Brazil.

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