Asymptotology: Ideas, Methods, and Applications: 551 (Mathematics and Its Applications, 551) - Hardcover

Andrianov, Igor V.; Manevitch, Leonid I.

Hardcover

ISBN 10: 1402009607 ISBN 13: 9781402009600

Publisher: Springer, 2002

Synopsis

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.

About this title

Review

"[...]quite interesting and should be informative for those wishing to gain some insight into the power of asymptotic methods and their pervasiveness in applied mathematics and the physical sciences without becoming too involved in their detailed mathematical description."
(Mathematical Reviews, 2003)

Synopsis

The main features of this volume are: 1) It is devoted to the basic principles of asymptotics and their applications; 2) It presents both traditional approaches as well as less widely used and new approaches such as one- and two-point Pade Approximants, constitutive equations, methods of boundary perturbations, etc.; 3) A general introduction to the subject suitable for non-specialists. Compared with other published books in the field the authors have paid special attention to examples and the discussion of results rather than burying them in formalism, in notation and in technical details. Audience: Researchers in mechanics, physics and applied mathematics as well as in engineering. Graduate students and even high school students can benefit from reading the book, which does not require any scientific knowledge of mathematics and physics.

Edition details

• Publisher: Springer
• Publication date: 2002
• Language: English
• ISBN 10: 1402009607
• ISBN 13: 9781402009600
• Binding: Hardcover
• Number of pages: 270