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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
From the reviews:
"This textbook presents a comprehensive and extremely well-organized treatment of its subject … . Verhulst’s monograph features an impressive clarity of exposition, giving the main and typical examples in a variety of related topics in singular perturbations, averaging, and multiple time scales, as manifested in various frameworks of ordinary and partial differential equations. The derivations are accompanied by enlightening explanations and by telling examples ... . I repeat my recommendation: This is a first-rate exposition which will be of much assistance to students and researchers." (Zvi Artstein, Mathematical Reviews, Issue 2006 k)
"Dutch applied mathematicians have contributed extensively to the development of singular perturbations theory and practice. … the new book by Verhulst also emphasizes averaging and a fine collection of challenging examples. … Readers … won’t be surprised to find a clear and lively presentation with enlightening historical commentary. … This year, I’m enthusiastic to use this new text in my singular perturbations course … ." (Robert O’Malley, Jr., SIAM Review, Vol. 48 (1), 2006)
"The reviewed monograph contains the historical introduction and auxiliary material on asymptotic convergence and asymptotic expansions, boundary layers and one example about the boundary of a laser-sustained plasma. ... Detailed illustrations, stimulating examples in every chapter make this monograph very useful for applied mathematicians in science and engineering fields." (Boris V. Loginov, Zentralblatt MATH, Vol. 1148, 2008)
Authors and Affiliations
Bibliographic Information
Book Title: Methods and Applications of Singular Perturbations
Book Subtitle: Boundary Layers and Multiple Timescale Dynamics
Authors: Ferdinand Verhulst
Series Title: Texts in Applied Mathematics
DOI: https://doi.org/10.1007/0-387-28313-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2005
Hardcover ISBN: 978-0-387-22966-9Published: 28 June 2005
Softcover ISBN: 978-1-4419-1992-2Published: 01 December 2010
eBook ISBN: 978-0-387-28313-5Published: 04 June 2006
Series ISSN: 0939-2475
Series E-ISSN: 2196-9949
Edition Number: 1
Number of Pages: XVI, 328
Topics: Ordinary Differential Equations, Partial Differential Equations, Mathematical Methods in Physics, Dynamical Systems and Ergodic Theory, Numerical Analysis, Applications of Mathematics