/sci/ - Science & Math

>>15159908
> high quality pedagogy to teach us modern calculus
> high quality ancient calculus books

The first statement is laughable. Calculus was something people used to solve problems rather informally until Fourier discovered the solutions to the heat equations, which involve a special series of trigonometric functions, but they couldn't be dealt with simply like the series people were used to. What grew out of that was Analysis, which formalized calculus because the old way of doing things didn't work.

This is all to say, calculus is something best guided by intuition, and those intuitions can than be formalized in an introduction to Analysis. Instead, this intuition is never built. What made me finally understand calculus was looking back at how people around the time of Newton and Euler though of calculus, and what motivated it in the first place.

For instance the number "e" came out of logarithm tables where it kept appearing. Taylor series are pretty easily derived as well. However the world calculus was born out of is gone, so learning it in the modern day is completely uninspired. It has reversed the process of discovery--->formalization. Only the worst kind of mental midget slave would find any appeal in memorizing a bunch of proofs and formulas while understanding none of them.

Pic related is my quick demonstration of an integral.