TY - BOOK
AU - Verhulst,Ferdinand
ED - SpringerLink (Online service)
TI - Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics
T2 - Texts in Applied Mathematics,
SN - 9780387283135
AV - QA372
U1 - 515.352 23
PY - 2005///
CY - New York, NY
PB - Springer New York
KW - Mathematics
KW - Dynamics
KW - Ergodic theory
KW - Differential equations
KW - Partial differential equations
KW - Applied mathematics
KW - Engineering mathematics
KW - Numerical analysis
KW - Physics
KW - Ordinary Differential Equations
KW - Partial Differential Equations
KW - Mathematical Methods in Physics
KW - Dynamical Systems and Ergodic Theory
KW - Numerical Analysis
KW - Applications of Mathematics
N1 - 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
N2 - 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
UR - http://dx.doi.org/10.1007/0-387-28313-7
ER -