物理科学中的奇异摄动（影印版）

样章

作者：

John C. Neu

定价：

135.00 元

版面字数：

550.00千字

开本：

特殊

装帧形式：

精装

页数：

344

最新
印次时间：

2025年01月

ISBN：

978-7-04-063249-1

物料号：

63249-00

出版时间：

2025-02-14

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

计算数学

暂无

目录
- 前辅文
- Acknowledgments
- Introduction
- Chapter 1. What is a singular perturbation?
  - Prototypical examples
    - Singularly perturbed polynomial equations
    - Radiation reaction
      - Problem 1.1: Bad truncations
      - Problem 1.2: Harmonic oscillator with memory, and even worse truncations
    - Convection-diffusion boundary layer
      - Problem 1.3: A simple boundary layer
      - Problem 1.4: Pileup near x = 0
    - Modulated oscillations
      - Problem 1.5: Secular terms
      - Problem 1.6: Approach to limit cycle
      - Problem 1.7: Adiabatic invariant for particle in a box
  - Guide to bibliography
- Chapter 2. Asymptotic expansions
  - Problem 2.1: Uniqueness
  - A divergent but asymptotic series
    - Problem 2.2: Divergent outer expansion
    - Problem 2.3: Another outrageous example
  - Asymptotic expansions of integrals — the usual suspects
    - Problem 2.4: Simple endpoint examples
    - Problem 2.5: Stirling approximation to n!
    - Problem 2.6: Endpoint and minimum both contribute
    - Problem 2.7: Central limit theorem
  - Steepest descent method
  - Chasing the waves with velocity v >0
  - No waves for v <0
    - Problem 2.8: Steepest descent asymptotics
  - A primer on linear waves
    - Problem 2.9: Amplitude transport
    - Problem 2.10: How far was that meteor?
    - Problem 2.11: Wave asymptotics in non-uniform medium
  - A hard logarithmic expansion
    - Problem 2.12: Logarithmic expansion
  - Guide to bibliography
- Chapter 3. Matched asymptotic expansions
  - Problem 3.1: Physical scaling analysis of boundary layer thickness
  - Problem 3.2: Higher-order matching
  - Problem 3.3: Absorbing boundary condition
  - Matched asymptotic expansions in practice
    - Problem 3.4: Derivative layer
  - Corner layers and internal layers
    - Problem 3.5: Phase diagram
    - Problem 3.6: Internal derivative layer
    - Problem 3.7: Where does the kink go?
  - Guide to bibliography
- Chapter 4. Matched asymptotic expansions in PDE’s
  - Moving internal layers
  - Chapman–Enskog asymptotics
    - Problem 4.1: Relaxation of kink position
    - Problem 4.2: Hamilton–Jacobi equation from front motion
    - Problem 4.3: Chapman–Enskog asymptotics
  - Projected Lagrangian
    - Problem 4.4: Circular fronts in nonlinear wave equation
    - Problem 4.5: Solitary wave dynamics in two dimensions
    - Problem 4.6: Solitary wave diffraction
  - Singularly perturbed eigenvalue problem
  - Homogenization of swiss cheese
    - Problem 4.7: Neumann boundary conditions and effective dipoles
    - Problem 4.8: Two dimensions
  - Guide to bibliography
- Chapter 5. Prandtl boundary layer theory
  - Stream function and vorticity
  - Preliminary non-dimensionalization
  - Outer expansion and “dry water”
  - Inner expansion
    - Problem 5.1: Vector calculus of boundary layer coordinates
  - Leading order matching and a first integral
    - Problem 5.2: The body surface is a source of vorticity
    - Problem 5.3: Downstream evolution
  - Displacement thickness
  - Solutions based on scaling symmetry
  - Blasius flow over flat plate
  - Nonzero wedge angles (m≠0)
  - Precursor of boundary layer separation
    - Problem 5.4: Wedge flows with source
    - Problem 5.5: Mixing by vortex
  - Guide to bibliography
- Chapter 6. Modulated oscillations
  - Physical flavors of modulated oscillations
    - Problem 6.1: Beats
    - Problem 6.2: The beat goes on
    - Problem 6.3: Wave packets as beats in spacetime
    - Problem 6.4: Adiabatic invariant of harmonic oscillator
    - Problem 6.5: Passage through resonance for harmonic oscillator
    - Problem 6.6: Internal resonance between waves on a ring
  - Method of two scales
    - Problem 6.7: Nonlinear parametric resonance
    - Problem 6.8: Forced van der Pol ODE
    - Problem 6.9: Inverted pendulum
  - Strongly nonlinear oscillations and action
    - Problem 6.10: Energy, action and frequency
    - Problem 6.11: Hamiltonian analysis of the adiabatic invariant
    - Problem 6.12: Poincar´e analysis of nonlinear oscillations
  - A primer on nonlinear waves
  - Modulation Lagrangian
    - Problem 6.13: Nonlinear geometric attenuation
    - Problem 6.14: Modulational instability
  - A primer on homogenization theory
    - Problem 6.15: Direct homogenization
  - Guide to bibliography
- Chapter 7. Modulation theory by transforming variables
  - Transformations in classical mechanics
    - Problem 7.1: Geometry of action-angle variables
    - Problem 7.2: Stokes expansion for quadratically nonlinear oscillator
    - Problem 7.3: Frequency-action relation
    - Problem 7.4: Follow the bouncing ball
  - Near-identity transformations
    - Problem 7.5: van der Pol ODE by near-identity transformations
    - Problem 7.6: Subtle balance between positive and negative damping
    - Problem 7.7: Adiabatic invariants again
  - Dissipative perturbations of the Kepler problem
  - Modulation theory of damped orbits
  - Guide to bibliography
- Chapter 8. Nonlinear resonance
  - Problem 8.1: Modulation theory of resonance
  - A prototype example
  - What resonance looks like
    - Problem 8.2: Resonance of the bouncing ball
    - Problem 8.3: Resonance by rebounds off a vibrating wall
  - Generalized resonance
  - Energy beats
  - Modulation theory of generalized resonance
    - Problem 8.4: Modulation theory for generalized resonance
  - Thickness of the resonance annulus
  - Asymptotic isolation of resonances
  - Guide to bibliography
- Bibliography
- Index

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物理科学中的奇异摄动（影印版）

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