Contemporary Mathematics 2005; 371 pp; softcover Volume: 373 ISBN10: 0821834193 ISBN13: 9780821834190 List Price: US$98 Member Price: US$78.40 Order Code: CONM/373
 The theory of analyzable functions is a technique used to study a wide class of asymptotic expansion methods and their applications in analysis, difference and differential equations, partial differential equations and other areas of mathematics. Key ideas in the theory of analyzable functions were laid out by Euler, Cauchy, Stokes, Hardy, E. Borel, and others. Then in the early 1980s, this theory took a great leap forward with the work of J. Écalle. Similar techniques and concepts in analysis, logic, applied mathematics and surreal number theory emerged at essentially the same time and developed rapidly through the 1990s. The links among various approaches soon became apparent and this body of ideas is now recognized as a field of its own with numerous applications. This volume stemmed from the International Workshop on Analyzable Functions and Applications held in Edinburgh (Scotland). The contributed articles, written by many leading experts, are suitable for graduate students and researchers interested in asymptotic methods. Readership Graduate students and research mathematicians interested in asymptotic methods. Table of Contents  S. AïtMokhtar  A singularly perturbed Riccati equation
 T. Aoki, T. Kawai, T. Koike, and Y. Takei  On global aspects of exact WKB analysis of operators admitting infinitely many phases
 M. Aschenbrenner and L. van den Dries  Asymptotic differential algebra
 W. Balser and V. Kostov  Formally wellposed Cauchy problems for linear partial differential equations with constant coefficients
 F. Blais, R. Moussu, and J.P. Rolin  Nonoscillating integral curves and ominimal structures
 B. Braaksma and R. Kuik  Asymptotics and singularities for a class of difference equations
 O. Costin  Topological construction of transseries and introduction to generalized Borel summability
 E. Delabaere  Addendum to the hyperasymptotics for multidimensional Laplace integrals
 F. Diener and M. Diener  Higherorder terms for the de MoivreLaplace theorem
 J. Ecalle  Twisted resurgence monomials and canonicalspherical synthesis of local objects
 A. Fruchard and E. Matzinger  Matching and singularities of canard values
 B. Mudavanhu and R. E. O'Malley, Jr.  On the renormalization method of Chen, Goldenfeld, and Oono
 S. P. Norton  Generalized surreal numbers
 C. Olivé, D. Sauzin, and T. M. Seara  Two examples of resurgence
