Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics

by Ferdinand Verhulst

Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this unique book deliniates boundary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in the context of the general theory, as well as a final discussion of the more advanced problems. Precise estimates and excursions into the theoretical background makes this workbook valuable to both the applied sciences and mathematics fields. As a bonus in its last chapter the book includes a collection of rare and useful pieces of literature, such as the summary of the Perturbation theory of Matrices.

Detailed illustrations, stimulating examples and exercises as well as a clear explanation of the underlying theory makes this workbook ideal for senior undergraduate and beginning graduate students in applied mathematics as well as science and engineering fields.

Kindle Edition

First published June 28, 2005

About the author

Ferdinand Verhulst is retired professor of Mathematics at the University of Utrecht in the Netherlands.

He is also the founder of the publisher Epsilon Uitgaven, in 1985. This publisher aims to publish scientific books in Dutch, with a special eye to Mathematics, both because it is easier to learn in your own language, and also to promote mathematics among non-mathematicians. In Dutch (as published on the website) "Epsilon Uitgaven beoogt het tot stand brengen en verspreiden van wetenschappelijke boeken in de Nederlandse taal met de nadruk op wiskunde."