close
1.

図書

図書
Ali Hasan Nayfeh
出版情報: New York : Wiley, c1981  xiv, 519 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Algebraic Equations
Integrals
The Duffing Equation
The Linear Damped Oscillator
Self-Excited Oscillators
Systems with Quadratic and Cubic Nonlinearities
General Weakly Nonlinear Systems
Forced Oscillations of the Duffing Equation
Multifrequency Excitations
The Mathieu Equation
Boundary-Layer Problems
Linear Equations with Variable Coefficients
Differential Equations with a Large Parameter
Solvability Conditions
Appendices
Bibliography
Index
Algebraic Equations
Integrals
The Duffing Equation
2.

図書

図書
J. Kevorkian, J.D. Cole
出版情報: New York : Springer-Verlag, c1981  x, 558 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 34
所蔵情報: loading…
3.

図書

図書
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
所蔵情報: loading…
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.:
4.

図書

図書
C.A.J. Fletcher
出版情報: New York : Springer-Verlag, c1984  xi, 309 p. ; 25 cm
シリーズ名: Springer series in computational physics
所蔵情報: loading…
5.

図書

図書
by Wei Shyy
出版情報: Amsterdam ; New York : Elsevier, 1994  xvii, 504 p. ; 25 cm
シリーズ名: Transport processes in engineering ; 5
所蔵情報: loading…
6.

図書

図書
Peter Henrici
出版情報: New York : Wiley, c1962  xi, 407 p. ; 24 cm
所蔵情報: loading…
7.

図書

図書
Karel Rektorys ; [translated from the Czech by Michael Basch]
出版情報: Dordrecht, Holland ; Boston, U.S.A. : D. Reidel Pub. Co., c1980  571 p. ; 28 cm
所蔵情報: loading…
8.

図書

図書
Bruce A. Finlayson
出版情報: New York : Academic Press, 1972  xiv, 412 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 87
所蔵情報: loading…
9.

図書

図書
Leon Lapidus and John H. Seinfeld
出版情報: New York : Academic Press, 1971  xii, 299 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 74
所蔵情報: loading…
10.

図書

図書
Steven E. Koonin
出版情報: Menlo Park, Calif. ; Tokyo : Benjamin/Cummings Pub. Co. , Redwood City, Calif. ; Tokyo : Addison-Wesley, c1986  x, 409 p. ; 25 cm
所蔵情報: loading…
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼