Limit Process Expansions Applied to Ordinary Differential Equations

In this chapter a series of simple examples are considered, some model and some physical, in order to demonstrate the application of various techniques concerning limit process expansions. In general we expect analytic dependence of the exact solution on the small parameter ε, but one of the main tasks in the various problems is to discover the nature of this dependence by working with suitable approximate differential equations. Another problem is to systematize as much as possible the procedures for discovering these expansions.