ABSTRACT
When solving differential equations in general, and partial differential equations in particular, it is necessary to express both the solution to the differential equation and the applied boundary conditions in the same form or “language” as each other. For example, in Chapter 6, we solved surface wave problems in which both the solution to the Laplace equation and the boundary condition at the free surface were expressed in terms of trigonometric functions. Sometimes we can obtain the solution to the differential equation in the form of an applied boundary condition, and on other occasions, we write the boundary condition in the same form as the solution to the differential equation. In both cases, we end up with a solution to the differential equation and to the applied boundary condition, both being in the same form or “language.”
