Asymptotology

Ideas, Methods, and Applications
2002
ISBN: 978-1-4020-0960-0
Verlag: Springer US

Buch, Englisch, Band 551, 252 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1240 g

Reihe: Mathematics and Its Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Manevitch, Leonid I.

Andrianov, Igor V.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Foreword. Preface. Acknowledgments. Synopsis.
1. Introduction.
2. What Are Asymptotic Methods?
3. A Little Mathematics.
4. How Asymptotic Methods Work.
5. Asymptotic Methods and Physical Theories.
6. Phenomenology and First Principles.
7. A Little History.
8. Fathers of Asymptotic Methods.
9. Conclusion.
Appendices: A. Linear and Nonlinear Mathematical Physics: from Harmonic Waves to Solitons.
B. Certain Mathematical Notions of Catastrophe Theory.
C. Asymptotics and Scaling Transformations.
D. Asymptotic Approaches: Attempt af a Definition.
E. Some Web-pages.
References.
About the Authors. Author Index.
Topic Index.