View source for Singular perturbation theory

==History and key ideas==

A great deal of the early motivation in this area arose from studies of physical
problems (O'Malley 1991, Cronin and O'Malley 1999).  Notable examples are:
  
* Poincare's work on time-scales for periodic phenomena in celestial mechanics  
* Prandtl's work on fluid flow (Van Dyke 1975)  
* van der Pol's work on electric circuits and oscillatory dynamics
* studies of biological systems and chemical reaction kinetics by Segel and others

Each of these areas yield problems whose solutions have features that
vary on disparate length- or time-scales.  The philosophy behind singular perturbation theory is to take
advantage of this separation of scales to obtain reduced problems that are
simpler than the original full problem.  Constructing an approximation of the full (global) solution of a singular problem in terms of the solutions of the reduced problems is a key element of the work in this field.