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)
Best Answer
Ryan, perhaps a bit unexpected is the application of calculus in the human heart. More precise, cardiac output. The definition of cardiac output is the volume of blood pumped by the heart per unit time. The formula for this turns out to be a Riemann sum which in turn becomes an integral. And I find that unexpected in the sense that most people will look for calculus applications in physics/engineering or perhaps economics. But who generally thinks about calculus at work in our own hearts?