Matched Asymptotic Expansions

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.