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,
Table of ContentsAsymptotology and Borel Summation: Asymptotics, Superasymptotics Hyperasymptotics; M. Berry. The Geometric Model of Crystal Growth: Numerical Analysis of the Geometric Model of Crystal Growth; J.M. Hammersley. Dendritic Crystal Growth: An Experimental Assessment of Continuum Models of Dendritic Growth; J.P. Gollub. Directional Solidification of Solids: Directional Growth of Dilute Mixtures and Lamellar Eutectics; K. Kassner, et al. Flow in a Hele-Shaw Cell: Viscous Displacement in a Hele-Shaw Cell; S. Tanveer. The Rapidly Forced Pendulum: Exponentially Small Estimate for Separatrix Splittings; J. Scheurle, et al. Ordinary Differential Equations: Singular Perturbations of Solitons; Y. Pomeau. Solitary Water Waves in the Presence of Small Surface Tension: Solitary Waves with Ripples Beyond All Orders; J.T. Beale. Problems in Optics. Potpourri. 23 additional articles. Index.