Ferdinand Verhulst (auth.)9780387229669, 0-387-22966-3
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.
Table of contents :
Introduction….Pages 1-7
Basic Material….Pages 9-23
Approximation of Integrals….Pages 25-30
Boundary Layer Behaviour….Pages 31-42
Two-Point Boundary Value Problems….Pages 43-62
Nonlinear Boundary Value Problems….Pages 63-76
Elliptic Boundary Value Problems….Pages 77-91
Boundary Layers in Time….Pages 93-120
Evolution Equations with Boundary Layers….Pages 121-142
The Continuation Method….Pages 143-163
Averaging and Timescales….Pages 165-186
Advanced Averaging….Pages 187-226
Averaging for Evolution Equations….Pages 227-247
Wave Equations on Unbounded Domains….Pages 249-266
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