Ferdinand Verhulst

Methods and Applications of Singular Perturbations (eBook, PDF)

Boundary Layers and Multiple Timescale Dynamics

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 328
• Erscheinungstermin: 4. Juni 2006
• Englisch
• ISBN-13: 9780387283135
• Artikelnr.: 43728559

Autorenporträt

Ferdinand Verhulst was born in Amsterdam and studied astrophysicist with a specialisation in numerical analysis. He spent five years at the Technical University of Delft, which stimulated his interest in theoretical engineering. Verhulst obtained his PhD from the University of Utrecht and became a Professor of Dynamical Systems there in 1990. He has been a visiting professor in prestigious universities worldwide and has completed five trips to Indonesia to teach mathematics, leading to three successful PhDs. Verhulst has authored numerous research papers and books, including five in English and two in Dutch, as well as edited two Springer Lecture Notes publications. Additionally, he founded Epsilon Uitgaven, a publishing house aimed at supporting teachers and students with Dutch language mathematics books, eventually contributing himself to a couple of their books, one on mathematical proofs and the other on chaos, both aimed at secondary school students.

Inhaltsangabe

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.

Rezensionen

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)