I for example us a great deal of differential equations when I'm developing audio and video filters (FIRs, IIRs etc...). I don't even have a math education past trig, the rest is from books and websites.
There are cases where I'd chose to perform real-time filter calculation for adaptive filters (things like calculating the points of an FIR without knowing my desired frequency response before hand), it's not terribly common outside of for example echo cancellation where I'd want to design the shortest possible filter with the desired effect for the current environment instead of just using a long filter with good response in all frequency ranges.
I generally do most of my math work in a tool like Matlab (sometimes Mathematica if it's more mathy and less computery) and then when I have the coefficients I desire for a formula, then I'll code it in C or C++... oddly sometimes in DSP assembler.
That said, another example of where I'm using calculus, though not terribly advanced calculus is that my 8 1/2 year daughter, 10 year old son and I are writing a platform scroller for their phones. The girl is doing pretty well with coding the object structure, my son is doing much of the artwork. I'm working mostly on things like motion. In the case of motion, I make use of rate of change calculations and apply them using simple physics. For example, if the user holds the right arrow for X amount of time, I increase the positive moment energy. If they press the left arrow it applies negative momentum energy, if they simply let go of the arrows, then at a given rate, the horizontal momentum energy reduces towards zero. For jumping, when the user presses space, depending on the duration, upward energy is applied until a peak is reached which will fight gravity. Gravity however works as expected 32feet *...
I also have used math a bit in producing a TDR for cable length detection.
Math is VERY useful in programming so long as you choose to work on projects where math is interesting :) Even when I was working for a web browser company, I'd find myself writing a JPEG decoder which isn't really hard math, but it's at least somewhat advanced.