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＜電子ブック＞
Multiple Scale and Singular Perturbation Methods / by J.K. Kevorkian, J.D. Cole
(Applied Mathematical Sciences. ISSN:2196968X ; 114)

版	1st ed. 1996.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1996
本文言語	英語
大きさ	VIII, 634 p : online resource
冊子体	Multiple scale and singular perturbation methods / J. Kevorkian, J.D. Cole
著者標目	*Kevorkian, J.K author Cole, J.D author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Mathematics LCSH:Mathematical physics LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 FREE:Analysis FREE:Applications of Mathematics FREE:Mathematical Methods in Physics FREE:Theoretical, Mathematical and Computational Physics FREE:Mathematical and Computational Engineering Applications
一般注記	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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-3968-0

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