Methods and Applications of Singular Perturbations

Boundary Layers and Multiple Timescale Dynamics

Ferdinand Verhulst - Collection Texts in Applied Mathematics

324 pages, parution le 31/03/2005

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Résumé

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.

Sommaire

Introduction
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
Appendices
Epilogue
Answers to Odd-Numbered Exercices
Literature
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Ferdinand Verhulst
Collection	Texts in Applied Mathematics
Parution	31/03/2005
Nb. de pages	324
Format	16 x 24
Couverture	Relié
Poids	605g
Intérieur	Noir et Blanc
EAN13	9780387229669
ISBN13	978-0-387-22966-9