The interesting part about Calculus, at least in the US, is that it is held in such high esteem. As if it is the pivotal accomplishment in a mathematical career. Calculus in many other educational systems is actually taught much earlier as a normal part of a mathematical curriculum (early high school in Russia, for example). Basic calculus is the look at a rate of change or a sensitivity to change as it relates to a change in the variables of a system (derivative). In other words an instantaneous rate of change would be a good example of a derivative (how fast does a rock fall from a building after it was dropped +2 seconds, or some such). The other area that is studied early is the idea of displacement, aka integrals. How much area is under a curve. More practically you can find things like the velocity from the rate of acceleration.

I know, I haven't answered your question yet. I have used Calculus, even much more advanced calculus, in computer science applications such as using it to calculate the salient region of interest in a photograph, for example. But in reality, I rarely use it. That being said, studying calculus and higher forms of mathematics have given me a broader sense of how to best solve problems. They give me the ability to see a problem and realize that brute force isn't the only answer to the problem. Mathematics shows that solutions can be nuanced and beautiful. Calculus is a good start in seeing that. Applying that ability to look at a problem and find nuanced and beautiful solutions is key to good software development.

Again, I am not sure that actually answers your question. But I find calculus to be mind expanding. I hope you'll enjoy it as much as I have.

Now if you'd like to see an actual application of calculus being used in computer science you might want to read about Richard Feynman at Thinking Machines Corporation: http://longnow.org/essays/richard-feynman-connection-machine... . One of the quotes from the article always makes me smile: "By the end of that summer of 1983, Richard had completed his analysis of the behavior of the router, and much to our surprise and amusement, he presented his answer in the form of a set of partial differential equations."

There is also a rather funny urban legend/joke about teaching Calculus in the US versus other countries:

"A certain well known mathematical from the USSR, we'll call him Professor P.T. (these are not his initials...), upon his arrival at Harvard University, was scheduled to teach Math 1a (the first semester of freshman calculus.) He asked his fellow faculty members what he was supposed to teach in this course, and they told him: limits, continuity, differentiability, and a little bit of indefinite integration.

The next day he came back and asked, 'What am I supposed to cover in the second lecture?'"

Enjoy learning Calculus!