This second video introduces some of the methods that engineers use to build control systems.  It shows how we use science to help us derive models of systems from both measurements and first principles.  These models often take the form of differential equations and engineers often use some other branches of math (linear algebra and/or transform theory) to convert these into simpler representations.  These simpler representations allow engineers to use algebra to gain insights into the original physical problem.  (The also answer the question that shows up in every middle school math class:  Will this stuff ever be useful for anything?)    The viewer need not know any of this math. We are merely showing it is on the path so folks don't think we made it all up. 

What is important is the idea that science gives us models which we turn into math.  We then simplify that math to make it actionable (hopefully preserving the essential behavior of the thing we were trying to model).  We then use that simplified math to give us insights that help us understand not only how to model something in the real world, but how to adjust it so it behaves better.