Abstract
We discuss methods for investigating the stability of parallel flows in a channel. The relationship between the Floquet spectrum and the initial value problem is made, and the solution to the Floquet problem is related to a pair of homogeneous integral equations equations involving the unknown vorticity and its derivative on the boundary over a period. For the semi-infinite classical Stokes layer problem, the Kernel of the integral equation is related to a PDE solution through use of generating functions. The asymptotics of this PDE solution for large Reynolds number is more ODE like and simplifies the expression for Kernel of the integral equation.