Comment on Can't forget unreasonable approximations either
I_am_10_squirrels@beehaw.org 1 day ago
I’m a licensed chemical engineer and mentoring junior engineers is what I enjoy most about being an engineer. If there’s anything in particular you’re looking for explanations of, I’m happy to help. If it’s not in my scope, I’ll do my best to learn it and explain it.
TwodogsFighting@lemdro.id 19 hours ago
Please sir, what the hell do differentials do?
NoneOfUrBusiness@fedia.io 19 hours ago
For the record you're presumably asking about derivatives (or, for the process, differentiation). A differential is just an infinitely small (infinitesimal is the term) change in some quantity. With that in mind, differentiation is how you take a function and get its rate of change (distance to speed is the usual example). You do this by essentially—and this is a theme with calculus—taking an approximation and making it so precise as to be exact. Specifically you take a small part of the curve and find its average rate of change, which is just the amount of change in the function divided by the amount of change in the independent variable. This is again an approximation, but if you make the part of the curve really really small the approximation becomes really really good until it's no longer an approximation. It's really just generalizing the idea of a slope to functions that aren't straight lines.
Does that make sense?
I_am_10_squirrels@beehaw.org 13 hours ago
Exactly this.
If you’re wondering why they’re useful, an example from my discipline is removing heat from a chemical reaction. You mix some ingredients together, stir for 2 hours, and you get a product. By combining the derivatives for the rate of reaction (how fast does A+B -> C) and the heat of reaction (how much energy does the reaction release), you can calculate how much cooling you need to prevent a runaway reaction that takes out half the neighborhood.