I've made my own simple physics engines and used linear algebra to do things like projecting from 3d to 2d space. None of it was any good but it was a lot of fun. This was back when I was most comfortable in Java and the performance was horrible. I don't know what methods of collision detection real engines use but Runge–Kutta is not a good option for real time games.

I don't know how to do it and make money but I would recommend playing with the math. It's like magic, you setup the formulas and things just start moving on the screen. It was so much fun.