Integration and the fundamental theorem of calculus | Chapter 8, Essence of calculus
What is an integral? How do you think about it? Check out the Art of Problem Solving: https://aops.com/3blue1brown Full series: http://3b1b.co/calculus Series ...
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This guy, Grothendieck, is somewhat of a mathematical idol to me. And I just love this quote, don’t you? Too often in math we just dive into showing that a certain fact is true with long series of formulas before stepping back and making sure that it feels reasonable, and preferably obvious, at least on an intuitive level. In this video I want to talk about integrals, and the thing that I want to become “almost obvious” is that they are an inverse of derivatives. Here, we’ll focus just on one example, which is kind of dual to the example of a moving car that I talked about in chapter 2 of the series, introducing derivatives. Then in the next video, we’ll see how the idea generalizes into some other contexts. Imagine you’re sitting in a car, and you can’t see out the window;...
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This guy, Grothendieck, is somewhat of a mathematical idol to me. And I just love this quote, don’t you? Too often in math we just dive into showing that a certain fact is true with long series of formulas before stepping back and making sure that it feels reasonable, and preferably obvious, at least on an intuitive level. In this video I want to talk about integrals, and the thing that I want to become “almost obvious” is that they are an inverse of derivatives. Here, we’ll focus just on one example, which is kind of dual to the example of a moving car that I talked about in chapter 2 of the series, introducing derivatives. Then in the next video, we’ll see how the idea generalizes into some other contexts. Imagine you’re sitting in a car, and you can’t see out the window;...
