alright just for fun: AMA but only about math, will attempt to speed-explain stuff with as few symbols and equations as possible and see what happens
(esp happy to field questions about stuff that seems basic to you and that you feel like you should've gotten a long time ago!)
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Diferential equations, how do they work? I understand theory behind integrals, derivatives and limits, but never learned diferential calculus.
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hmm. can you be more specific? like how do we write them down or how do we solve them or something else?
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I have seen them written down, and I am like, what is this small delta doing here? And how do I deal with two variables?
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so, for intuition, you can think of differential equations as difference equations where the difference is really small. a simple example of a difference equation is like
f(x + 1) - f(x) = g(x)
and you solve it by summing: f(x) = g(0) + g(1) + ... + g(x-1)
the corresponding simplest example of a differential equation is like
f'(x) = g(x)
which is sort of an infinitesimal version of the difference equation, and you solve it by integrating: f(x) = int g(x), the continuous analog of summing