Math for Programmers

12 Optimizing a physical system

This chapter covers

• Building and visualizing a simulation for a projectile
• Finding maximal and minimal values for a function using derivatives
• Tuning simulations with parameters
• Visualizing spaces of input parameters for simulations
• Implementing gradient ascent to maximize functions of several variables

For most of the last few chapters, we’ve focused on a physical simulation for a video game. This is a fun and simple example to work with, but there are far more important and lucrative applications. For any big feat of engineering like sending a rocket to Mars, building a bridge, or drilling an oil well, it’s important to know that it’s going to be safe, successful, and on budget before you attempt it. In each ...