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Perturbation Methods in Applied Mathematics (Hardcover, 1st ed. 1981. Corr. 2nd printing 1985)
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Perturbation Methods in Applied Mathematics (Hardcover, 1st ed. 1981. Corr. 2nd printing 1985)
Series: Applied Mathematical Sciences, 34
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This book is a revised and updated version, including a substantial
portion of new material, of J. D. Cole's text Perturbation Methods
in Applied Mathe matics, Ginn-Blaisdell, 1968. We present the
material at a level which assumes some familiarity with the basics
of ordinary and partial differential equations. Some of the more
advanced ideas are reviewed as needed; therefore this book can
serve as a text in either an advanced undergraduate course or a
graduate level course on the subject. The applied mathematician,
attempting to understand or solve a physical problem, very often
uses a perturbation procedure. In doing this, he usually draws on a
backlog of experience gained from the solution of similar examples
rather than on some general theory of perturbations. The aim of
this book is to survey these perturbation methods, especially in
connection with differ ential equations, in order to illustrate
certain general features common to many examples. The basic ideas,
however, are also applicable to integral equations,
integrodifferential equations, and even to_difference equations. In
essence, a perturbation procedure consists of constructing the
solution for a problem involving a small parameter B, either in the
differential equation or the boundary conditions or both, when the
solution for the limiting case B = 0 is known. The main
mathematical tool used is asymptotic expansion with respect to a
suitable asymptotic sequence of functions of B."
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