Ask HN: Adult learning Calc

For fun in my free time I'm writing a game in unity and c# where you pilot a plane. I could not find an auto pilot script so i am writing it from scratch.

While trying to figure out how to dynamically set the planes elevator deflection based on the planes vertical speed and distance from the desired altitude i discovered that writing an auto pilot involves some advanced math :)

My math resume ends at high school trig.

I am hoping to discover what flavor of math should i focus my studies on to achieve my goal and possibly hoping to avoid learning any fluff in the process.

Thanks all