In mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory. In simpler terms, the definition of a pseudo-differential operator depends on the Fourier Transform. This topic is actually covered long after the introduction of the Fourier Transform. The Fourier Transform is covered at varying levels of rigor beginning with a cursory introduction in a standard second year differential equations course focusing on applications...