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Preface ·
Errata ·
Table of Contents
Multiple Scale and Singular Perturbation Methods
Preface
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 5. Near Identity Averaging Transformation;
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
Chapter 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
Index
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Multiple Scale ... ·
Books ·
J. Kevorkian ·