I've yet to see calculus applied by any programming.
How does your laptop computer calculate remaining battery life?
How does your browser calculate remaining download time?
Neither of these seems an obvious application for calculus. Both can be done very simply with a trivial calculation, but for some odd reason they very seldom are.
For the download one, the calculation simply is, "How much of the download is done? How long did it take? Assume the rest will happen at the same rate and extrapolate."
I itch to re-write the firmware in our photocopier at school, which estimates the time for a job right at the beginning (always a bit optimistically), and then simply counts down, ignoring the progress which it's made. This leads to it estimating, say, 25 mins for a job, and then counting down over the next 25 mins, with the result that when it has done 80% of the job its estimated time remaining reaches zero and stays there for the remaining 6 and a bit minutes. It would be trivial to re-write this code properly, and I hate the fact that I can't do it.
Kyocera - step forward in shame.