4 ms·
the issue i take with the way most calculus is taught is starting with limits and derivatives. this is not the way humans discovered calculus. we discovered int
by officialjunk 12y ago
the issue i take with the way most calculus is taught is starting with limits and derivatives. this is not the way humans discovered calculus. we discovered integral calculus (finding the area under a curve) a couple thousand years earlier. it is really cool that derivatives and integration are inverse operations, but starting with integration is in my opinion easier to grasp and derive formulas the student already knows: area of square, triangle, circle, etc. once that gap is closed, then introducing derivatives makes more sense.
- xamuel 12y agoDepends on the definition of calculus. Without the fundamental theorem (which absolutely requires differentiation), explicitly calculating those areas is unreasonably hard (undoable in all but the simplest cases, and in the cases where it is doable, you usually have to be Archimedes to do it). Sure, you could start the course with numerical integration, but this really wouldn't help anything else. (You might be interested, though, to know that your suggestion is essentially how higher math is sometimes done. The natural logarithm function is defined by ln(x)=int_1^x(1/x)dx, which if you look closely doesn't involve exponentials in any way, allowing you to non-circularly define the exponential function as the inverse of the logarithm function, and once you've got the exponential function, the game is on)