A physics engine is a software component that is meant to simulate or enhance some sort of real life property in a video game. This can include things like rigid body dynamics, some computer graphics, and gravity. It can simulate collisions as well. If it involves physics this engine can simulate it. (within reason)
There are many real world equations used in these games. However, some of these equations are simply too exact for the game it is being used on. This means that the equations must be modified or completely replaced to fit within the limits of the game.
An example of this: an object is flying through the air and hits a wall between two frames. Since the game only sees what happens within those frames, the game doesn't detect a collision and the object goes right through it. To compensate, the objects velocity must be adjusted as well as the equation used to tell if it hits the wall. It must produce consistent numbers among all objects it applies to, AND it must be detectable within the frames the game is running at. The higher a games frames, the easier these equations are.
In conclusion, math is very important in physics engines, but the math does not match the real world math most of the time. That's okay though, after all, since its just a game.
This page by Levi M. ('19)