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

ISBN-13: 9781441919922 / Angielski / Miękka / 2010 / 328 str.

Ferdinand Verhulst

Opis

Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Recenzje

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)

Spis treści

Basic Material.- Approximation of Integrals.- Boundary Layer Behaviour.- Two-Point Boundary Value Problems.- Nonlinear Boundary Value Problems.- Elliptic Boundary Value Problems.- Boundary Layers in Time.- Evolution Equations with Boundary Layers.- The Continuation Method.- Averaging and Timescales.- Advanced Averaging.- Averaging for Evolution Equations.- Wave Equations on Unbounded Domains.

O autorze

Perturbation theory is a fascinating and fundamental topic in mathematics and its applications to the natural and engineering sciences. In this workbook, each explicit example is studied and methods introduced, beginning without proof, a learning method very suitable for singular perturbation problems. The text includes an extensive discussion of timescales and apriori knowledge of the presence of certain timescales. This comprehensive introduction to singular perturbation covers a broad range of topics, includes odes' and pde's, boundary value problems, and problems with initial values.

Blurb

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.