To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.

Readership

Advanced undergraduates, graduate students, and applied mathematicians interested in ordinary differential equations.

Table of Contents

• R. E. O'Malley, Jr. -- Figuring out singular perturbations after a first course in ODEs
• M. H. Holmes -- The method of multiple scales
• S. Adjerid, M. Aiffa, and J. E. Flaherty -- Computational methods for singularly perturbed systems
• T. J. Kaper -- An introduction to geometric methods and dynamical systems theory for singular perturbation problems
• J. Cronin -- Analysis of cellular oscillations
• M. J. Ward -- Exponential asymptotics and convection-diffusion-reaction models
• Index