Generally a particular physical

system has a generalized set of governing

equations that describe its phenomena. For example,

Maxwell's Equations completely describe the behavior of

electric and

magnetic fields in a

global sense.

To solve a certain problem it sometimes becomes necessary to further solve or reduce the governing equations to study a particular system. This is often done by considering the system under study, and noting its boundary conditions, or a priori knowledge of the variable of interest at the boundary of the system. Having this knowledge, solutions to the equation can often be derived that are particular to that certain type of problem. For example, the boundary conditions that the electric field must satisfy at the walls of a waveguide constrain the solution of Maxwell's Equations to a very small set of equations which are more commonly known as the waveguide's modes.

In a more general sense, there are several types of boundary conditions. Consider a variable *v*. These conditions are commonly referred to in the following manner:

Knowledge of the variable's value and its derivatives at the boundaries forms the heart of **Boundary Value Problems**.