As an example of how calculus is useful in game design, imagine you have an object you want to move into a position. However, instead of just moving at a constant speed and snapping into place, you want it to start out fast and kinda "slide" into place at the end, smoothly.

To start out, you might want to plot its position as a function of time, and a semi parabola works perfectly for us. In addition, you know that its speed will start out at some value, and decrease to zero at the final point. Understanding that velocity is the derivative of position (stick with me), you can link these two functions together and with some set conditions like distance and desired time to complete, you can calculate the initial speed and acceleration you should give your object to reach the target with your desired movement. To apply this in gamemaker, you would calculate the initial speed and gravity using the above method, and then set an alarm to stop it after the number of ticks you want, and the math handles the rest! (And did I mention it looks real neat!)

This is what you learn in the 100-level math course "Calculus I with Analytic Geometry", which is the study of functions and how you can shape them to have desired properties. Very neat stuff, and incredibly helpful when dealing with physics calculations.

Additionaly, if you're interested in learning more about math and how it applies to game design, TJ's doing some on-stream math lessons! Here's his first one,

Distances, Triangles, and Trig: For Game Makers!