MULTIPLE SCALE AND SINGULAR PERTURBATION METHODS (HB 1996)
KEVORKIAN J K
ISBN 10: 0387942025 ISBN 13: 9780387942025
Editore: SPRINGER, 1996
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This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981).
Contenuti: 1. Introduction.- 1.1. Order Symbols, Uniformity.- 1.2. Asymptotic Expansion of a Given Function.- 1.3. Regular Expansions for Ordinary and Partial Differential Equations.- References.- 2. Limit Process Expansions for Ordinary Differential Equations.- 2.1. The Linear Oscillator.- 2.2. Linear Singular Perturbation Problems with Variable Coefficients.- 2.3. Model Nonlinear Example for Singular Perturbations.- 2.4. Singular Boundary Problems.- 2.5. Higher-Order Example: Beam String.- References.- 3. Limit Process Expansions for Partial Differential Equations.- 3.1. Limit Process Expansions for Second-Order Partial Differential Equations.- 3.2. Boundary-Layer Theory in Viscous, Incompressible Flow.- 3.3. Singular Boundary Problems.- References.- 4. The Method of Multiple Scales for Ordinary Differential Equations.- 4.1. Method of Strained Coordinates for Periodic Solutions.- 4.2. Two Scale Expansions for the Weakly Nonlinear Autonomous Oscillator.- 4.3. Multiple-Scale Expansions for General Weakly Nonlinear Oscillators.- 4.4. Two-Scale Expansions for Strictly Nonlinear Oscillators.- 4.5. Multiple-Scale Expansions for Systems of First-Order Equations in Standard Form.- References.- 5. Near-Identity Averaging Transformations: Transient and Sustained Resonance.- 5.1. General Systems in Standard Form: Nonresonant Solutions.- 5.2. Hamiltonian System in Standard Form; Nonresonant Solutions.- 5.3. Order Reduction and Global Adiabatic Invariants for Solutions in Resonance.- 5.4. Prescribed Frequency Variations, Transient Resonance.- 5.5. Frequencies that Depend on the Actions, Transient or Sustained Resonance.- References.- 6. Multiple-Scale Expansions for Partial Differential Equations.- 6.1. Nearly Periodic Waves.- 6.2. Weakly Nonlinear Conservation Laws.- 6.3. Multiple-Scale Homogenization.- References.
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Titolo: MULTIPLE SCALE AND SINGULAR PERTURBATION ...
Casa editrice: SPRINGER
Data di pubblicazione: 1996
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Condizione: New
Edizione: Edizione Internazionale
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Multiple Scale and Singular Perturbation Methods
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Hardcover. Condizione: Very Good. Text is unmarked; pages are bright. Binding is tight and square. Upper corners are bumped. 634pp. Codice articolo 056707
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Multiple Scale and Singular Perturbation Methods (Applied Mathematical Sciences, 114)
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Multiple Scale and Singular Perturbation Methods (Applied Mathematical Sciences, 114)
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Springer (edition 1996), 1996
ISBN 10: 0387942025
ISBN 13: 9780387942025
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Hardcover. Condizione: Very Good. 1996. It's a well-cared-for item that has seen limited use. The item may show minor signs of wear. All the text is legible, with all pages included. It may have slight markings and/or highlighting. Codice articolo 0387942025-8-1
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Multiple Scale and Singular Perturbation Methods
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Hardcover. Condizione: Very Good. Condizione sovraccoperta: None Issued. Text is unmarked; pages are bright, though the page edges are scuffed and smudged. The base of the spine is bumped; the binding still feels sturdy. The corners of the covers are also bumped. No dust jacket, as issued. 632pp. Codice articolo 066142
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Multiple Scale and Singular Perturbation Methods (Applied Mathematical Sciences, 114)
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ISBN 10: 0387942025
ISBN 13: 9780387942025
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Multiple Scale and Singular Perturbation Methods (Applied Mathematical Sciences, 114)
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Multiple Scale and Singular Perturbation Methods
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Condizione: Sehr gut. Zustand: Sehr gut | Seiten: 648 | Sprache: Englisch | Produktart: Bücher | This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter. Codice articolo 1275015/202
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