Asymptotic methods belong to the, perhaps, most romantic area of modern
mathematics. They are widely known and have been used in me- chanics,
physics and other exact sciences for many, many decades. But more than
this, asymptotic ideas are found in all branches of human knowledge,
indeed in all areas of life. In this broader context they have not and
perhaps cannot be fully formalized. However, they are mar- velous, they
leave room for fantasy, guesses and intuition; they bring us very near
to the border of the realm of art. Many books have been written and
published about asymptotic meth- ods. Most of them presume a
mathematically sophisticated reader. The authors here attempt to
describe asymptotic methods on a more accessi- ble level, hoping to
address a wider range of readers. They have avoided the extreme of
banishing formulae entirely, as done in some popular science books that
attempt to describe mathematical methods with no mathematics. This is
impossible (and not wise). Rather, the authors have tried to keep the
mathematics at a moderate level. At the same time, using simple
examples, they think they have been able to illustrate all the key ideas
of asymptotic methods and approaches, to depict in de- tail the results
of their application to various branches of knowledg- from astronomy,
mechanics, and physics to biology, psychology and art. The book is
supplemented by several appendices, one of which con- tains the profound
ideas of R. G.
