OK, I feel challenged.
Calculus in a thread https://twitter.com/ChemistryKit/status/1260519315742359554
Imagine I have some business and I have so much profit every month. I can graph that. Now I want to know how much I've made this year - and hey, it turns out it's just the area under this graph.
But is it important that I use months?
If I use weeks I get less money in each period, but there's more periods - so it turns out no, it doesn't matter. And you can make the periods as short as you want. Now for a store this gets crazy - a car dealer makes nothing most minutes, then a big spike.
But for physics problems it usually works well - I drive at some varying speed, the distance I've gone is the area under the curve.
But the area depends on what time it is, (I keep driving). So the area's a function of time. (yup, my position's a function of time)
So really, I want to convert one function (my speed/monthly profit) to another one (my position/total profit). A process called integration. Lots of tricks u learn in calc class, then forget all but a few.
Integral of X^n is (X ^(n+1))/(n+1)
Integral of sin(X) is cos(X)
integral of cos(X) is sin(X)
and find a table of integrals otherwise.
Nobody really does these manually any more, there are programs.
What about the other way? Sometimes how fast things change is important - if my driving ends with slowing from 80 to 0 in 1 second I'm having a very bad day. The rate of change of a value is the opposite of integration - differentiation.
So, Liebniz and Newton each thought this all up, then Newton went on to propose the laws of basic physics, based on it. position <-> speed <-> acceleration. force is mass * acceleration. integrate force thru distance you get work, change in energy, and energy is conserved.
The crazy writing's not that hard - the big S is for 'sum' and means integrate. The little dx at the end is to remind us that Liebniz and Newton were both incredible dicks.
Differentiation's d(whatever)/dx, which reminds us that being open to change is better than being a couple dicks, even if we're dumber than rocks and they're smart enough to invent calculus.
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