Calc 1: Differential Calculus

Lecture 6: Preview of Calculus

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In this video, we talk about two of the motivations for developing calculus: Finding tangent lines and computing velocity. These were historically two of the motivations behind the development of calculus. There is a third, which I did not include in the video. The third motivation is determining the area under a curve. People have been trying to determine the area of geometric shapes at least as far back as Archimedes in the 200s BCE. It was Archimedes who first discovered the formula for the area of a circle that we all take for granted now. I didn't include the discussion about area under a curve, because that is more of an integral calculus topic, but you can find a really good discussion of it in this video by 3Blue1Brown.

I highly recommend you watch 3Blue1Brown's "Essence of Calculus" video series (linked just above). The videos in that series are better than mine, because 3Blue1Brown knows how to make really good (and helpful!) animations, and I don't.