Methods and Applications of Singular Perturbations [electronic resource] : Boundary Layers and Multiple Timescale Dynamics / by Ferdinand Verhulst.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Texts in Applied Mathematics: 50Publisher: New York, NY : Springer New York, 2005Description: XVI, 328 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387283135Subject(s): Mathematics | Dynamics | Ergodic theory | Differential equations | Partial differential equations | Applied mathematics | Engineering mathematics | Numerical analysis | Physics | Mathematics | Ordinary Differential Equations | Partial Differential Equations | Mathematical Methods in Physics | Dynamical Systems and Ergodic Theory | Numerical Analysis | Applications of MathematicsAdditional physical formats: Printed edition:: No titleDDC classification: 515.352 LOC classification: QA372Online resources: Click here to access online
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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.
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.