Asymptotics of Slow-time Processes, First Steps
In this chapter we shall discuss those concepts and elementary methods in asymptotics which are necessary prerequisites for the study of slow-time processes in nonlinear oscillations. In considering a function defined by an integral or defined as the solution of a differential equation with boundary or initial conditions, approximation techniques can be useful. In the applied mathematics literature no single theory dominates but many techniques can be found based on a great variety of concepts leading in general to different results. We mention here the methods of numerical analysis, approximation by orthonormal function series in a Hilbert space, approximation by convergent series and the theory of asymptotic approximations. Each of these methods can be suitable to understand an explicitly given problem. In this book we consider problems where the theory of asymptotic approximations is useful and we introduce the necessary concepts in detail.
KeywordsPeriodic Solution Standard Form Nonlinear Oscillation Asymptotic Approximation Order Function
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