Comment by Animats
7 hours ago
Calculus is entry level math for all the hard sciences, engineering, and finance. It's how to think about how things change over time. Understanding what integrals and derivatives look like, especially as graphs, is very practical knowledge. Being able to think about compound interest and acceleration under gravity as driven by the same rules gives an understanding of what's happening underneath.
Whether the infinite-series summation limits are worth knowing is questionable, though. That's more of historical interest.
(But then, I once did a game physics engine and have a patent in that area. I spent a lot of time in the hell which is integration of stiff systems of nonlinear differential equations. Turned out that was the wrong way to approach the problem. Works, but there are better approaches.)
My grad program had an advanced math sequence that was traditionally numerical methods for solving PDE’s and boundary value problems. Except my year, a visiting professor made it infinite series solutions using laplace transforms. Because why would you want an inexact numerical solution when you could have an exact solution to whatever degree of accuracy you need. Line integrals have their own special place in hell.
> Whether the infinite-series summation limits are worth knowing is questionable, though. That's more of historical interest.
A very common example is compound, continual interest accumulation. As a mathematician, I had trouble understanding how banks calculate it (as they would obviously not point me at the derivation of the formula), but it's actually a limit sum over infinitely small interest terms.
Similarly, these techniques work to explain and derive numerical methods for calculating many natural constants like e, pi etc.
The only intuitive definition of e I can remember is "how much $1 becomes after a year in a savings account with 100% interest compounded infinitely" funny enough.
That definition also gives a nice introduction to e's taylor series!
Right? Just because my professional career never took me in those directions doesn't mean I want to foreclose them for my kid! I did do electrical engineering classes in college wherein I needed calculus, I just never took a derivative/integral after graduation because I ended up on the coding side of a Computer Engineering degree.