  A differential geometric approach to singular perturbation theory is
presented. It is shown that singular perturbation problems such as
multiple-scale and boundary layer problems can be treated more easily on a
differential geometric basis. A general method is proposed based on
differential forms and Lie-derivatives. Examples from multiple scale theory,
boundary layer theory and WKB-theory are given and it is demonstrated that
without the a priori knowledge of the scaling behaviour of the problem the
correct asymptotic expansion can be derived with the aid of differential forms.
The method is well suited for a mechanical implementation in computer algebra
programs.
