Calculus is basically the study of how functions change over time. Velocity is an example : it is the rate of change of your position over time.
It is a very elaborate subject, and has many applications. The two most important ones are the ability to find extreme values (minimum / maximum) of functions and the ability to estimate how good an approximation really is.
In the general professional pilot community, these are reflected in tables, graphs, and rules of thumb, so that you don't see calculus at work. Indeed, many professional pilots just learn those rules by heart and just look at graphs, or trust their computers / calculators when the result of a formula pops up.
People who are good at calculus (and who understand the applications) have an easier job at remembering formulas or the shapes of curves, because they understand the mechanics behind it. That has helped me in sitting some of the career exams, and it allowed me to write some flight planning software myself. But in all honesty, you would rarely use calculus directly in flight.
the world has misjudged pilots
The general public still reveres the pilot community, seeing pilots as the pinnacle of both intelligence and skill.
Nevertheless, especially since the introduction of low cost airlines, the market (driving pilots' pay) has a more accurate perception of what a professional pilot brings to the table: that is, a medically fit and responsible human being that has completed a 12-18 month specialized (expensive) training. But they are not engineers, they don't have an MBA and it is not a given that they have good interpersonal or management skills.