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FOREWORD

The importance of mathematics in the study of problems arising from the real world,
and the increasing success with which it has been used to model situations ranging
from the purely deterministic to the stochastic, is well established. The purpose of the
set of volumes to which the present one belongs is to make available authoritative, up
to date, and self-contained accounts of some of the most important and useful of these
analytical approaches and techniques. Each volume provides a detailed introduction to
a specific subject area of current importance that is summarized below, and then goes
beyond this by reviewing recent contributions, and so serving as a valuable reference
source.
The progress in applicable mathematics has been brought about by the extension and
development of many important analytical approaches and techniques, in areas both
old and new, frequently aided by the use of computers without which the solution of
realistic problems would otherwise have been impossible.
A case in point is the analytical technique of singular perturbation theory which
has a long history. In recent years it has been used in many different ways, and its
importance has been enhanced by it having been used in various fields to derive
sequences of asymptotic approximations, each with a higher order of accuracy than its
predecessor. These approximations have, in turn, provided a better understanding of
the subject and stimulated the development of new methods for the numerical solution
of the higher order approximations. A typical example of this type is to be found in
the general study of nonlinear wave propagation phenomena as typified by the study
of water waves.