Calculus shows up in a lot of places in the world. Specifically, here are three areas where I see it used the most:
- Optimization problems.
- Anything involving rates of change (e.g. velocity $\rightarrow$ acceleration).
- Anything involving "averages" (e.g. surface area).
I am more interested in the non-intuitive and unexpected applications of Calculus, however. For instance, the Fourier Transform is an alright example. But in some ways I still feel like Calculus isn't totally unexpected here, as it becomes really intuitive once you understand that the integral is just computing the average power at each signal frequency.
So, in what fields/areas of science does Calculus pop up unexpectedly? Preferably those applications which are practical in the real world. (i.e. not number theory)