Before English physicist and mathematician Sir Isaac Newton's time, physicists experimented using simple mathematical calculations. Physics and related sciences actually began to develop after Newton and Gottfried Wilhelm Leibniz devised calculus.

Mathematical physics uses the laws of physics and the differential method of calculus to set up equations for the system being studied. The resulting differential equations can then be solved or analyzed. The tools of mathematics are calculus and other advanced mathematics, such as complex analysis. Many scientists have contributed to mathematical physics in the past several hundred years. Equations in mathematical physics were often named after those scientists who discovered them. The central topics of mathematical physics are the differential equations, or the partial differential equations (PDE). There are three classes of partial differential equations.

The first class is called the wave equation,

where c is the speed of the wave and ƒ is...