Sophisticated engines could not even happen until Maxwell’s use of dif- ferential equations in order to stop the engines of that time from flying apart, stopping, or oscillating wildly, so the mathematics here starts with advanced calculus. Today’s engines are far more sophisticated. Their designs require the solutions of complex non-linear partial differential equations and very advanced work with linear algebra. Today a major focus is on autonomous machines, machines that can do routine and even non-routine tasks without human control. They will do the most repetitive jobs, for example automating the assembly line and the most dangerous jobs
