Content and Aims of this Book Earlier drafts of the manuscript of
this book (James A. Boa was then coau thor) contained discussions
of many methods and examples of singular perturba tion problems.
The ambitious plans of covering a large number of topics were later
abandoned in favor of the present goal: a thorough discussion of
selected ideas and techniques used in the method of matched
asymptotic expansions. Thus many problems and methods are not
covered here: the method of av eraging and the related method of
multiple scales are mentioned mainly to give reasons why they are
not discussed further. Examples which required too sophis ticated
and involved calculations, or advanced knowledge of a special
field, are not treated; for instance, to the author's regret some
very interesting applications to fluid mechanics had to be omitted
for this reason. Artificial mathematical examples introduced to
show some exotic or unexpected behavior are omitted, except when
they are analytically simple and are needed to illustrate
mathematical phenomena important for realistic problems. Problems
of numerical analysis are not discussed."
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