An equation which involves partial derivatives of a function f(x, y) (or f(x,t) or f(x,y,z), etc.) is called a partial differential equation or simply a POE. The study of PDE's could easily fill an entire semester course by itself. Deriving solutions to PDE_s and understanding the implications of a solution can be challenging. For the purposes of this course, you should know two things:
i) the physical basis underlying a specific PDE, and
ii) given a function, you should be able to verify whether or not it satisfies a specific PDE.