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1.

図書
図書
1. Advanced mathematical methods for scientists and engineers
Carl M. Bender, Steven A. Orszag
出版情報: New York ; Tokyo : McGraw-Hill, c1978  xiv, 593 p. ; 25 cm
シリーズ名: International series in pure and applied mathematics
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2.

図書
図書
2. Numerical quadrature and solution of ordinary differential equations : a textbook for a beginning course in numerical analysis (: us : softcover ; : gw)
A.H. Stroud
出版情報: New York : Springer-Verlag, 1974  xi, 338 p. ; 26 cm
シリーズ名: Applied mathematical sciences ; v. 10
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3.

図書
図書
3. Stable recursions : with applications to the numerical solution of stiff systems
J. R. Cash
出版情報: London ; New York : Academic Press, 1979  xii, 223 p. ; 24 cm
シリーズ名: Computational mathematics and applications
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4.

図書
図書
4. Computational methods in ordinary differential equations
J.D. Lambert
出版情報: London ; New York : Wiley, c1973  xv, 278 p. ; 24 cm
シリーズ名: Introductory mathematics for scientists and engineers
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5.

図書
図書
5. Analysis of discretization methods for ordinary differential equations (: us ; : gw)
Hans J. Stetter
出版情報: Berlin ; New York : Springer, 1973  xvi, 388 p. ; 24 cm
シリーズ名: Springer tracts in natural philosophy ; v. 23
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6.

図書
図書
6. Coupled modes in plasmas, elastic media, and parametric amplifiers : a numerical method
[by] Eugene D. Denman
出版情報: New York : American Elsevier Pub. Co., 1970  236 p ; 24 cm
シリーズ名: Modern analytic and computational methods in science and mathematics ; v. 27
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7.

図書
図書
7. 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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8.

図書
図書
8. Modern numerical methods for ordinary differential equations
edited by G. Hall and J. M. Watt
出版情報: Oxford : Clarendon Press, 1976  336 p. ; 25 cm
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9.

図書
図書
9. Similarity methods for differential equations (: softcover)
G.W. Bluman, J.D. Cole
出版情報: New York : Springer-Verlag, 1974  ix, 332 p. ; 26 cm
シリーズ名: Applied mathematical sciences ; v. 13
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10.

図書
図書
10. Sommerfeldsche Polynommethode (: gw ; : us)
A. Rubinowicz
出版情報: Berlin ; New York : Springer , Warszawa : Polnischer Verlag der Wissenschaften, 1972  xiv, 278 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 185
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11.

図書
図書
11. Partielle differentialgleichungen erster Ordnung für eine gesuchte Function. 3rd, unaltered ed
von E. Kamke
出版情報: New York : Chelsea Pub. Co. , New York : Bronx, 1974  243 p. ; 24 cm
シリーズ名: Differentialgleichungen : Lösungsmethoden und Lösungen / von E. Kamke ; 2
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目次情報:
D. Differentialgleichungen erster Ordnung fur eine gesuchte Funktion: Allgemeine Vorbemerkungen Die Lineare homogene Differentialgleichung $f(x, y)\frac{\partial z}{\partial x} + g(x, y)\frac{\partial z}{\partial y}=0$ Die allgemeine lineare homogene Differentialgleichung $\sum f_v (x_1,\dots, x_n)\frac{\partial z}{\partial x_v}=0$ Die allgemeine lineare Differentialgleichung $\sum f_v (x_1, \dots, x_n)\frac{\partial z}{\partial x_v}+ f_0 (x_1, \dots, x_n)z=f(x_1,\dots, x_n)$ Die quasilineare Differentialgleichung $\sum f_v(x_1,\dots, x_n, z)\frac{\partial z}{\partial x_v}=g(x_1, \dots, x_n, z)$ Systeme linearer Differentialgleichungen Systeme quasilinearer Differentialgleichungen Einleitende Bemerkungen Losungsverfahren von Lagrange Existenzsatze und weitere Losungsverfahren Losungsverfahren fur einige Sonderfalle Die Differentialgleichung $F(x_1,\dots, x_n, z,\frac{\partial z}{\partial x_1}, \dots, \frac{\partial z}{\partial x_n})=0$ Losungsverfahren fur einige Sonderfalle Systeme von Differentialgleichungen E. Einzel-Differentialgleichungen: Vorbemerkungen $F(x, y, z, p)=0$ Lineare und quasilineare Differentialgleichungen mit zwei unabhangigen Veranderlichen Lineare und quasilineare Differentialgleichungen mit drei unabhangigen Veranderlichen Lineare und quasilineare Differentialgleichungen mit vier und mehr unabhangigen Veranderlichen Systeme von linearen und quasilinearen Differentialgleichungen Nichtlineare Differentialgleichungen mit zwei unabhangigen Veranderlichen Nichtlineare Differentialgleichungen mit drei unabhangigen Veranderlichen Nichtlineare Differentialgleichungen mit mehr als drei unabhangigen Veranderlichen Systeme von nichtlinearen Differentialgleichungen Register
D. Differentialgleichungen erster Ordnung fur eine gesuchte Funktion: Allgemeine Vorbemerkungen Die Lineare homogene Differentialgleichung $f(x, y)\frac{\partial z}{\partial x} + g(x, y)\frac{\partial z}{\partial y}=0$ Die allgemeine lineare homogene Differentialgleichung $\sum f_v (x_1,\dots, x_n)\frac{\partial z}{\partial x_v}=0$ Die allgemeine lineare Differentialgleichung $\sum f_v (x_1, \dots, x_n)\frac{\partial z}{\partial x_v}+ f_0 (x_1, \dots, x_n)z=f(x_1,\dots, x_n)$ Die quasilineare Differentialgleichung $\sum f_v(x_1,\dots, x_n, z)\frac{\partial z}{\partial x_v}=g(x_1, \dots, x_n, z)$ Systeme linearer Differentialgleichungen Systeme quasilinearer Differentialgleichungen Einleitende Bemerkungen Losungsverfahren von Lagrange Existenzsatze und weitere Losungsverfahren Losungsverfahren fur einige Sonderfalle Die Differentialgleichung $F(x_1,\dots, x_n, z,\frac{\partial z}{\partial x_1}, \dots, \frac{\partial z}{\partial x_n})=0$ Losungsverfahren fur einige Sonderfalle Systeme von Differentialgleichungen E. Einzel-Differentialgleichungen: Vorbemerkungen $F(x, y, z, p)=0$ Lineare und quasilineare Differentialgleichungen mit zwei unabhangigen Veranderlichen Lineare und quasilineare Differentialgleichungen mit drei unabhangigen Veranderlichen Lineare und quasilineare Differentialgleichungen mit vier und mehr unabhangigen Veranderlichen Systeme von linearen und quasilinearen Differentialgleichungen Nichtlineare Differentialgleichungen mit zwei unabhangigen Veranderlichen Nichtlineare Differentialgleichungen mit drei unabhangigen Veranderlichen Nichtlineare Differentialgleichungen mit mehr als drei unabhangigen Veranderlichen Systeme von nichtlinearen Differentialgleichungen Register
12.

図書
図書
12. 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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13.

図書
図書
13. The method of weighted residuals and variational principles : with application in fluid mechanics, heat and mass transfer
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
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14.

図書
図書
14. Numerical solution of ordinary differential equations
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
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15.

図書
図書
15. 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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16.

図書
図書
16. Almost periodic differential equations (: Germany ; : U.S.)
A.M. Fink
出版情報: Berlin ; New York : Springer-Verlag, 1974  viii, 336 p ; 25 cm
シリーズ名: Lecture notes in mathematics ; 377
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17.

図書
図書
17. Numerical and quantitative analysis
G. Fichera ; translated from the Italian by Sandro Graffi
出版情報: London ; San Francisco : Pitman, 1978  x, 208 p. ; 26 cm
シリーズ名: Surveys and reference works in mathematics / main editors, A. Jeffrey, R.G. Douglas ; 3
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18.

図書
図書
18. Invariant imbedding and its applications to ordinary differential equations : an introduction (pbk.)
[by] Melvin R. Scott
出版情報: Reading, Mass. : Addison-Wesley Pub. Co., Advanced Book Program, 1973  xvii, 215 p ; 24 cm
シリーズ名: Applied mathematics and computation : a series of graduate textbooks, monographs, reference works / Series Editor Robert Kalaba ; no. 1
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19.

図書
図書
19. 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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