Asymptotology

1. Front Matter

   Pages i-xvii

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2. Introduction

   • Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel

   Pages 1-6

3. What Are Asymptotic Methods?

   • Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel

   Pages 7-39

4. A Little Mathematics

   • Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel

   Pages 41-80

5. How Asymptotic Methods Work

   • Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel

   Pages 81-102

6. Asymptotic Methods and Physical Theories

   • Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel

   Pages 103-117

7. Phenomenology and First Principles

   • Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel

   Pages 119-127

8. A Little History

   • Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel

   Pages 129-136

9. Fathers of Asymptotic Methods

   • Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel

   Pages 137-178

10. Conclusion. Homo Analiticus or Homo Computicus? Homo Asymptoticus!

    • Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel

    Pages 179-182

11. Back Matter

    Pages 183-252

    PDF

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.

• Mathematica
• applied mathematics
• history of mathematics
• perturbation
• perturbation theory

"[...]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)

• Pridneprovie State Academy of Civil Engineering and Architecture (PGASA), Dnepropetrovsk, Ukraine

  Igor V. Andrianov

• N.N. Semenov Institute for Chemical Physics of Russian Academy of Sciences, Moscow, Russia

  Leonid I. Manevitch

• CWI (Center for Mathematics and Computer Science), Amsterdam, The Netherlands

  Michiel Hazewinkel

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