Methods and Applications of Singular Perturbations

• 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.

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)