Asymptotics beyond All Orders

  • Harvey Segur
  • Saleh Tanveer
  • Herbert Levine

Part of the NATO ASI Series book series (NSSB, volume 284)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Asymptotology and Borel Summation

  3. The Geometric Model of Crystal Growth

  4. Dendritic Crystal Growth

  5. Directional Solidification of Solids

    1. K. Kassner, C. Misbah, H. Müller-Krumbhaar, Y. Saito, D. E. Temkin
      Pages 105-118
    2. A. Libchaber, A. J. Simon, J.-M. Flesselles
      Pages 119-129
  6. Flow in a Hele-Shaw Cell (Also known as VISCOUS FINGERING)

    1. S. Tanveer
      Pages 131-153
    2. Martine Ben Amar, Roland Combescot
      Pages 155-173
  7. The Rapidly Forced Pendulum

    1. Jürgen Scheurle, Jerrold E. Marsden, Philip Holmes
      Pages 187-195
    2. Martin Kummer, James A. Ellison, A. W. Sáenz
      Pages 197-211
  8. Ordinary Differential Equations

  9. Solitary Water Waves in the Presence of Small Surface Tension

    1. Jean-Marc Vanden-Broeck
      Pages 275-291
    2. M. C. Shen, S. M. Sun
      Pages 299-307
  10. Problems in Optics

    1. Ann Kahlow Hobbs, William L. Kath, Gregory A. Kriegsmann
      Pages 309-316
    2. Olivier Martin, Spiros V. Branis
      Pages 327-336
  11. Potpourri

  12. Back Matter
    Pages 385-389

About this book


An asymptotic expansion is a series that provides a sequence of increasingly accurate approximations to a function in a particular limit. The formal definition, given by Poincare (1886, Acta Math. 8:295), is as follows. Given a function,


Renormalization group bifurcation differential equation experiment geometry invariant numerical analysis optics ordinary differential equation oscillation partial differential equation reflection solution stability symmetry

Editors and affiliations

  • Harvey Segur
    • 1
  • Saleh Tanveer
    • 2
  • Herbert Levine
    • 3
  1. 1.University of ColoradoBoulderUSA
  2. 2.Ohio State UniversityColumbusUSA
  3. 3.University of CaliforniaSan Diego, La JollaUSA

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag US 1991
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-0437-2
  • Online ISBN 978-1-4757-0435-8
  • Series Print ISSN 0258-1221
  • Buy this book on publisher's site