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Chapter 8 addresses the intial value problem, x, where the effect of initial conditions are sought within the linear disturbance regime. Laplace transforms, moving coordinates and numerical approaches are all discussed. Examples of the latter include channel flows and the Blasius boundary layer. The chapter concludes with an in-depth discussion of optimizing the initial conditions for subcritical Reynolds numbers to obtain the maximum energy as a function of time. The concept of algebraically instability is discussed within this context, such that when the normalized energy density is greater than one, the flow is said to be algebraically unstable.