Differential equations

Differential equations rule the world!  Well, it's not that simple.  You see, differential equations explain the world around us.  Every physical process seems to have a differential equation behind it.  For example Maxwell's equations explain the classical behavior of electrically charged particles.  Even Newton's famous "F=ma" is a differential equation.  Notice that a stands for acceleration which is nothing but a second derivative.  If Newton is too simple for you, then you should study Lagrangian mechanics.  Lagrangian mechanics is a more general way of solving classical problems.

Oh, if you're not happy with only a classical study of nature, you may want to study quantum mechanics.  Guess what, there's a differential equation behind that to.  Quantum mechanics does influence the real world.  The so-called "Electron leak problem" is explained by quantum mechanics.  This "problem" means that there is a limit on how small traditional computers can get.  Once a computer gets too small it's darn near impossible to keep an electron where you want it.  Noticed I used the term "traditional computers" that's because maybe with a better understanding of quantum mechanics one could make a computer we only dream of today.  Quantum mechanics also helps explain the properties of matter.

There are other phenomena which are not classical in nature.  These are explained by special and general relativity.  Special relativity doesn't have any differential equations behind it, but it alters Newton's differential equations and makes them harder to solve.  General relativity, well it has differential equations behind it, a whole new kind of differential equation.

These are reasons people who study the natural sciences want to understand differential equations.  Differential equations also are used in the study of engineering, economics, biological science, epidemiology, and probably a host of subjects that I'm leaving out.

Differential equations really do rule the world.  Good thing they don't have an agenda.