Asymptotology

Ideas, Methods, and Applications

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

Part of the Mathematics and Its Applications book series (MAIA, volume 551)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel
    Pages 1-6
  3. Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel
    Pages 7-39
  4. Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel
    Pages 41-80
  5. Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel
    Pages 81-102
  6. Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel
    Pages 103-117
  7. Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel
    Pages 119-127
  8. Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel
    Pages 129-136
  9. Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel
    Pages 137-178
  10. Igor V. Andrianov, Leonid I. Manevitch, Michiel Hazewinkel
    Pages 179-182
  11. Back Matter
    Pages 183-252

About this book

Introduction

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.

Keywords

Mathematica applied mathematics history of mathematics perturbation perturbation theory

Authors and affiliations

  • Igor V. Andrianov
    • 1
  • Leonid I. Manevitch
    • 2
  • Michiel Hazewinkel
    • 3
  1. 1.Pridneprovie State Academy of Civil Engineering and Architecture (PGASA)DnepropetrovskUkraine
  2. 2.N.N. Semenov Institute for Chemical Physics of Russian Academy of SciencesMoscowRussia
  3. 3.CWI (Center for Mathematics and Computer Science)AmsterdamThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-9162-1
  • Copyright Information Springer-Verlag US 2002
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-4816-0
  • Online ISBN 978-1-4419-9162-1
  • About this book