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1.

図書
図書
1. Asymptotic analysis (: us ; : gw)
J.D. Murray
出版情報: New York ; Tokyo : Springer-Verlag, c1984  vi, 164 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 48
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2.

図書
図書
2. Global theory of a second order linear ordinary differential equation with a polynomial coefficient
Yasutaka Sibuya
出版情報: Amsterdam : North-Holland Pub. Co. , New York : American Elsevier Pub. Co., 1975  xv, 290 p. ; 24 cm
シリーズ名: North-Holland mathematics studies ; 18
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3.

図書
図書
3. Asymptotics and special functions
F.W.J. Olver
出版情報: New York : Academic Press, 1974  xvi, 572 p. ; 24 cm
シリーズ名: Computer science and applied mathematics : a series of monographs and textbooks
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4.

図書
図書
4. Matched asymptotic expansions : ideas and techniques (: U.S ; : Germany)
P.A. Lagerstrom
出版情報: New York ; Tokyo : Springer-Verlag, c1988  xii, 250 p. ; 24 cm
シリーズ名: Applied mathematical sciences ; v. 76
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5.

図書
図書
5. Matched asymptotic expansions and singular perturbations (: North-Holland ; : American Elsevier)
Wiktor Eckhaus
出版情報: Amsterdam : North-Holland Pub. Co. , New York : American Elsevier Pub. Co., 1973  145 p. ; 24 cm
シリーズ名: North-Holland mathematics studies ; 6
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6.

図書
図書
6. Perturbation methods
Ali Hasan Nayfeh
出版情報: New York : Wiley, c1973  xii, 425 p. ; 23 cm
シリーズ名: Pure and applied mathematics
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目次情報: 続きを見る
Introduction / 1.：
Parameter Perturbations / 1.1.：
An Algebraic Equation / 1.1.1.：
The van der Pol Oscillator / 1.1.2.：
Coordinate Perturbations / 1.2.：
The Bessel Equation of Zeroth Order / 1.2.1.：
A Simple Example / 1.2.2.：
Order Symbols and Gauge Functions / 1.3.：
Asymptotic Expansions and Sequences / 1.4.：
Asymptotic Series / 1.4.1.：
Asymptotic Expansions / 1.4.2.：
Uniqueness of Asymptotic Expansions / 1.4.3.：
Convergent versus Asymptotic Series / 1.5.：
Nonuniform Expansions / 1.6.：
Elementary Operations on Asymptotic Expansions / 1.7.：
Exercises
Straightforward Expansions and Sources of Nonuniformity / 2.：
Infinite Domains / 2.1.：
The Duffing Equation / 2.1.1.：
A Model for Weak Nonlinear Instability / 2.1.2.：
Supersonic Flow Past a Thin Airfoil / 2.1.3.：
Small Reynolds Number Flow Past a Sphere / 2.1.4.：
A Small Parameter Multiplying the Highest Derivative / 2.2.：
A Second-Order Example / 2.2.1.：
High Reynolds Number Flow Past a Body / 2.2.2.：
Relaxation Oscillations / 2.2.3.：
Unsymmetrical Bending of Prestressed Annular Plates / 2.2.4.：
Type Change of a Partial Differential Equation / 2.3.：
Long Waves on Liquids Flowing down Incline Planes / 2.3.1.：
The Presence of Singularities / 2.4.：
Shift in Singularity / 2.4.1.：
The Earth-Moon-Spaceship Problem / 2.4.2.：
Thermoelastic Surface Waves / 2.4.3.：
Turning Point Problems / 2.4.4.：
The Role of Coordinate Systems / 2.5.：
The Method of Strained Coordinates / 3.：
The Method of Strained Parameters / 3.1.：
The Lindstedt-Poincare Method / 3.1.1.：
Transition Curves for the Mathieu Equation / 3.1.2.：
Characteristic Exponents for the Mathieu Equation (Whittaker's Method) / 3.1.3.：
The Stability of the Triangular Points in the Elliptic Restricted Problem of Three Bodies / 3.1.4.：
Characteristic Exponents for the Triangular Points in the Elliptic Restricted Problem of Three Bodies / 3.1.5.：
A Simple Linear Eigenvalue Problem / 3.1.6.：
A Quasi-Linear Eigenvalue Problem / 3.1.7.：
The Quasi-Linear Klein-Gordon Equation / 3.1.8.：
Lighthill's Technique / 3.2.：
A First-Order Differential Equation / 3.2.1.：
The One-Dimensional Earth-Moon-Spaceship Problem / 3.2.2.：
A Solid Cylinder Expanding Uniformly in Still Air / 3.2.3.：
Expansions by Using Exact Characteristics--Nonlinear Elastic Waves / 3.2.4.：
Temple's Technique / 3.3.：
Renormalization Technique / 3.4.：
Limitations of the Method of Strained Coordinates / 3.4.1.：
The Methods of Matched and Composite Asymptotic Expansions / 3.5.1.：
The Method of Matched Asymptotic Expansions / 4.1.：
Introduction--Prandtl's Technique / 4.1.1.：
Higher Approximations and Refined Matching Procedures / 4.1.2.：
A Second-Order Equation with Variable Coefficients / 4.1.3.：
Reynolds' Equation for a Slider Bearing / 4.1.4.：
The Method of Composite Expansions / 4.1.5.：
A Second-Order Equation with Constant Coefficients / 4.2.1.：
An Initial Value Problem for the Heat Equation / 4.2.2.：
Limitations of the Method of Composite Expansions / 4.2.4.：
Variation of Parameters and Methods of Averaging / 5.：
Variation of Parameters / 5.1.：
Time-Dependent Solutions of the Schrodinger Equation / 5.1.1.：
A Nonlinear Stability Example / 5.1.2.：
The Method of Averaging / 5.2.：
Van der Pol's Technique / 5.2.1.：
The Krylov-Bogoliubov Technique / 5.2.2.：
The Generalized Method of Averaging / 5.2.3.：
Struble's Technique / 5.3.：
The Krylov-Bogoliubov-Mitropolski Technique / 5.4.：
The Duffiing Equation / 5.4.1.：
The Klein-Gordon Equation / 5.4.2.：
The Method of Averaging by Using Canonical Variables / 5.5.：
The Mathieu Equation / 5.5.1.：
A Swinging Spring / 5.5.3.：
Von Zeipel's Procedure / 5.6.：
Averaging by Using the Lie Series and Transforms / 5.6.1.：
The Lie Series and Transforms / 5.7.1.：
Generalized Algorithms / 5.7.2.：
Simplified General Algorithms / 5.7.3.：
A Procedure Outline / 5.7.4.：
Algorithms for Canonical Systems / 5.7.5.：
Averaging by Using Lagrangians / 5.8.：
A Model for Dispersive Waves / 5.8.1.：
A Model for Wave-Wave Interaction / 5.8.2.：
The Nonlinear Klein-Gordon Equation / 5.8.3.：
The Method of Multiple Scales / 6.：
Description of the Method / 6.1.：
Many-Variable Version (The Derivative-Expansion Procedure) / 6.1.1.：
The Two-Variable Expansion Procedure / 6.1.2.：
Generalized Method--Nonlinear Scales / 6.1.3.：
Applications of the Derivative-Expansion Method / 6.2.：
Forced Oscillations of the van der Pol Equation / 6.2.1.：
Parametric Resonances--The Mathieu Equation / 6.2.4.：
The van der Pol Oscillator with Delayed Amplitude Limiting / 6.2.5.：
Limitations of the Derivative-Expansion Method / 6.2.6.：
Limitations of This Technique / 6.3.：
Generalized Method / 6.4.：
A General Second-Order Equation with Variable Coefficients / 6.4.1.：
A Linear Oscillator with a Slowly Varying Restoring Force / 6.4.3.：
An Example with a Turning Point / 6.4.4.：
The Duffing Equation with Slowly Varying Coefficients / 6.4.5.：
Reentry Dynamics / 6.4.6.：
Advantages and Limitations of the Generalized Method / 6.4.7.：
Asymptotic Solutions of Linear Equations / 7.：
Second-Order Differential Equations / 7.1.：
Expansions Near an Irregular Singularity / 7.1.1.：
An Expansion of the Zeroth-Order Bessel Function for Large Argument / 7.1.2.：
Liouville's Problem / 7.1.3.：
Higher Approximations for Equations Containing a Large Parameter / 7.1.4.：
Homogeneous Problems with Slowly Varying Coefficients / 7.1.5.：
Reentry Missile Dynamics / 7.1.7.：
Inhomogeneous Problems with Slowly Varying Coefficients / 7.1.8.：
Successive Liouville-Green (WKB) Approximations / 7.1.9.：
Systems of First-Order Ordinary Equations / 7.2.：
Expansions Near an Irregular Singular Point / 7.2.1.：
Asymptotic Partitioning of Systems of Equations / 7.2.2.：
Subnormal Solutions / 7.2.3.：
Systems Containing a Parameter / 7.2.4.：
Homogeneous Systems with Slowly Varying Coefficients / 7.2.5.：
The Langer Transformation / 7.3.：
Problems with Two Turning Points / 7.3.3.：
Higher-Order Turning Point Problems / 7.3.4.：
Higher Approximations / 7.3.5.：
An Inhomogeneous Problem with a Simple Turning Point--First Approximation / 7.3.6.：
An Inhomogeneous Problem with a Simple Turning Point--Higher Approximations / 7.3.7.：
An Inhomogeneous Problem with a Second-Order Turning Point / 7.3.8.：
Turning Point Problems about Singularities / 7.3.9.：
Turning Point Problems of Higher Order / 7.3.10.：
Wave Equations / 7.4.：
The Born or Neumann Expansion and The Feynman Diagrams / 7.4.1.：
Renormalization Techniques / 7.4.2.：
Rytov's Method / 7.4.3.：
A Geometrical Optics Approximation / 7.4.4.：
A Uniform Expansion at a Caustic / 7.4.5.：
The Method of Smoothing / 7.4.6.：
References and Author Index
Subject Index
Introduction / 1.：
Parameter Perturbations / 1.1.：
An Algebraic Equation / 1.1.1.：
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