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1.

図書
図書
1. Continuous and discrete dynamics near manifolds of equilibria (: gw ; : us)
Bernd Aulbach
出版情報: Berlin ; New York : Springer-Verlag, 1984  ix, 142 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1058
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2.

図書
図書
2. 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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3.

図書
図書
3. Introduction to perturbation techniques
Ali Hasan Nayfeh
出版情報: New York : Wiley, c1981  xiv, 519 p. ; 24 cm
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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
4.

図書
図書
4. Numerical methods for differential equations and applications
Liviu Gr. Ixaru
出版情報: Bucuresti, Romania : Editura Academiei , Dordrecht : D. Reidel, c1984  xxi, 337 p. ; 23 cm
シリーズ名: Mathematics and its applications ; East European series
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5.

図書
図書
5. 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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6.

図書
図書
6. 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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7.

図書
図書
7. 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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8.

図書
図書
8. Computational Galerkin methods (: New York ; : Berlin)
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
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9.

図書
図書
9. The Numerical solution of nonlinear problems
edited by Christopher T.H. Baker and Chris Phillips
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 1981  viii, 369 p. ; 25 cm
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10.

図書
図書
10. Approximate methods for solution of differential and integral equations
by S.G. Mikhlin and K.L. Smolitskiy ; translated by Scripta Technica ; translation editor, Robert E. Kalaba
出版情報: New York : American Elsevier Pub., c1967  xi, 308 p. ; 24 cm
シリーズ名: Modern analytic and computational methods in science and mathematics ; v. 5
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11.

図書
図書
11. Elementary stability and bifurcation theory (: New York ; : Berlin)
Gérard Iooss, Daniel D. Joseph
出版情報: New York : Springer-Verlag, c1980  xv, 286 p. ; 24 cm
シリーズ名: Undergraduate texts in mathematics
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Asymptotic Solutions of Evolution Problems
Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension
Imperfection Theory and Isolated Solutions Which Perturb Bifurcation
Stability of Steady Solutions of Evolution Equations in Two Dimensions and n Dimensions. Appendices
Bifurcation of Steady Solution in Two Dimensions and the Stability of the Bifurcating Solutions. Appendix
Methods of Projection for General Problems of Bifurcation into Steady Solutions
Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions
Bifurcation of Periodic Solutions in the General Case
Subharmonic Bifurcation of Forced T-Periodic Solutions
Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions. Appendices
Secondary Subharmonic and Symptotically Quasi-Periodic Bifurcation of Periodic Solutions (of Hopf's Type) in the Autonomous Case
Stability and Bifurcation in Conservative Systems
Asymptotic Solutions of Evolution Problems
Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension
Imperfection Theory and Isolated Solutions Which Perturb Bifurcation
12.

図書
図書
12. 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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13.

図書
図書
13. Pathways to solutions, fixed points, and equilibria
W.I. Zangwill, C.B. Garcia
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1981  xv, 479 p. ; 24 cm
シリーズ名: Prentice-Hall series in computational mathematics
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14.

図書
図書
14. 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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15.

図書
図書
15. Time domain electromagnetics
edited by S.M. Rao
出版情報: San Diego ; Tokyo : Academic Press, 1999  xi, 372 p. ; 26 cm
シリーズ名: Academic Press series in engineering
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目次情報: 続きを見る
Preface
Acknowledgments
Contributors
Introduction / Miller1.：
An Initial Exploration of Time Domain Phenomena / 1.1：
The Infinite-Length Wire Antenna / 1.1.1：
The Finite-Length Wire Antenna / 1.1.2：
The Finite-Length Wire Scatterer / 1.1.3：
Late-Time Radiation from an Impulsively Excited Perfect Conductor / 1.1.4：
Some Special Capabilities of Time Domain Models / 1.1.5：
Modeling Chocies in CEM / 1.2：
Why Model in the Time Domain? / 1.2.1：
Evolution of Time Domain Modeling / 1.2.2：
Some General References / 1.2.3：
General Aspects of Time Domain Modeling / 1.3：
Model Development / 1.3.1：
Explicit vs Implicit Solution / 1.3.2：
Excitation Requirements / 1.3.3：
TD Solution / 1.3.4：
Time Domain Integral Equation Modeling / 1.4：
Some Representative TDIEs / 1.4.1：
A Prototype TDIE Model / 1.4.2：
Alternate Forms for a TDIE Solution / 1.4.3：
Excitation of a TDIE Model / 1.4.4：
Physical Implication of a TDIE Explicit Model / 1.4.5：
A Near-Neighbor TD Approximation / 1.4.6：
Time Domain Differential Equation Modeling / 1.5：
Space-Time Sampling of TDDE / 1.5.1：
Some Spatial-Mesh Alternatives / 1.5.2：
Mesh Closure Conditions / 1.5.3：
Handling Small Features in DE Models / 1.5.4：
Obtaining Far Fields from DE Models / 1.5.5：
Variations of TDDE Models / 1.5.6：
Comparison of TDDE and TDIE Models / 1.5.7：
Specific Issues Related to Time Domain Modeling / 1.6：
Increasing the Stability of the Time-Stepping Solution / 1.6.1：
Exploiting EM Singularities / 1.6.2：
Signal Processing as a Part of TD Modeling / 1.6.3：
Total-Field and Scattered-Field Formulations / 1.6.4：
Handling Frequency Dispersion and Loading in TD Models / 1.6.5：
Handling Medium and Component Nonlinearities or Time Variations in TD Models / 1.6.6：
Hybrid TD Models / 1.6.7：
The Concept of Pseudo-Time in Iterative FD Solutions / 1.6.8：
Exploiting Symmetries in TD Modeling / 1.6.9：
Concluding Remarks / 1.7：
Bibliography
Wire Structures: TDIE Solution / Rao ; Sarkar2.：
Basic Analysis / 2.1：
Analysis of a Straight Wire / 2.2：
Method of Moments Solution / 2.2.1：
Conjugate Gradient Method Solution / 2.2.2：
Numerical Example / 2.2.3：
Analysis of an Arbitrary Wire / 2.3：
Moment Method Solution / 2.3.1：
Conjugate Gradient Method / 2.3.2：
Numerical Examples / 2.3.3：
Implicit Solution Scheme / 2.4：
Application to Arbitrary Wire / 2.4.1：
Numerical Implementation / 2.4.2：
Analysis of Multiple Wires and Wire Junctions / 2.4.3：
Infinite Conducting Cylinders: TDIE Solution / Vechinski2.6：
Integral Equation Formulation / 3.1：
Discretization Scheme / 3.2：
TM Incidence: EFIE Formulation / 3.3：
Explicit Solution Procedure / 3.3.1：
Implicit Solution Procedure / 3.3.2：
TE Incidence: EFIE Formulation / 3.3.3：
TE Incidence: HFIE Formulation / 3.4.1：
Finite Conducting Bodies: TDIE Solution / 3.5.1：
Numerical Solution Scheme / 4.1：
Explicit Numerical Method / 4.2.1：
Implicit Numerical Method / 4.2.2：
Efficiency Considerations / 4.2.3：
Far-Scattered Fields / 4.2.4：
Near-Scattered Fields / 4.3.1：
Extrapolation of Time Domain Response / 4.5：
Matrix Pencil Method / 4.5.1：
Total Least Squares Matrix Pencil / 4.5.2：
Dielectric Bodies: TDIE Solution / 4.5.3：
Two-Dimensional Cylinders / 5.1：
Numerical Solution Procedure / 5.2.1：
Three-Dimensional Bodies / 5.2.2：
Finite-Difference Time Domain Method / Umashankar5.3.1：
Introduction to FDTD / 6.1：
Pulse Propagation in a Lossy, Inhomogeneous, Layered Medium / 6.2：
Propagation of Half-Sine Pulse / 6.2.1：
Remote Sensing of Inhomogeneous, Lossy, Layered Media / 6.3：
Profile Inversion Results / 6.3.1：
Key Elements of FDTD Modeling Theory / 6.4：
FDTD Formulation for Two-Dimensional Closed-Region Problems / 6.5：
FDTD Formulation for TM and TE Cases / 6.5.1：
Hollow Rectangular Waveguide / 6.5.2：
Dielectric Slab-Loaded Rectangular Waveguide / 6.5.3：
Shielded Microstrip Lines / 6.5.4：
FDTD Formulation for Two-Dimensional Open-Region Problems / 6.6：
Absorbing Radiation Boundary Condition / 6.6.1：
Second-Order Radiation Boundary Condition / 6.6.2：
Plane Wave Source Condition / 6.7：
Near- to Far-Field Transformation / 6.8：
FDTD Modeling of Curved Surfaces / 6.9：
Perfectly Conducting Object: The TE Case / 6.9.1：
Perfectly Conducting Object: The TM Case / 6.9.2：
Homogeneous Dielectric Object: The TE Case / 6.9.3：
FDTD Formulation for Three-Dimensional Closed-Region Problems / 6.10：
Three-Dimensional Full-Wave Analysis / 6.10.1：
Compact Two-Dimensional FDTD Algorithm / 6.10.2：
Evaluation of Dispersion Characteristics / 6.10.3：
FDTD Formulation for Three-Dimensional Open-Region Problems / 6.11：
Three-Dimensional Plane Wave Source Condition / 6.11.1：
Near- to Far-Field Transformation for the Three-Dimensional Case / 6.12：
RCS of a Flat-Plate Scatterer / 6.12.1：
Computer Resources and Modeling Implications / 6.13：
Transmission Line Modeling Method / Gothard ; German6.14：
The Two-Dimensional TLM / 7.1：
Time Domain Wave Equation / 7.1.1：
Time Domain Transmission Line Equation / 7.1.2：
Equating Maxwell's and the Circuit Equations / 7.1.3：
General Scattering Matrix Theory / 7.1.4：
Applying Scattering Theory to the Free-Space Shunt T-Line / 7.1.5：
Modeling Inhomogeneous Lossy Media / 7.1.6：
Excitation of the TLM Mesh and Metallic Boundaries / 7.1.7：
TLM Mesh Truncation Conditions / 7.1.8：
Discretization of the TLM Spatial Grid / 7.1.9：
TLM Output / 7.1.10：
The Series Node and Duality / 7.1.11：
Outline of the Algorithm for Two-Dimensional TLM Code / 7.1.12：
Three-Dimensional TLM / 7.2：
Special Features in TLM / 7.3：
Frequency-Dependent Material / 7.3.1：
Alternative Meshing Schemes / 7.3.2：
Antenna Array / 7.4：
Electromagnetic Scattering / 7.4.2：
Finite-Element Time Domain Method / Roy ; Salazar-Palma ; Djordjevic7.5：
Incident Field / 8.1：
Transverse Magnetic Case / 8.2：
Formulation / 8.2.1：
Finite-Element Procedure / 8.2.2：
Time-Stepping Procedure / 8.2.3：
Numerical Results / 8.2.4：
Transverse Electric Case / 8.3：
Finite-Volume Time Domain Method / Bonnet ; Ferrieres ; Michielsen ; Klotz ; Roumiguieres8.3.1：
Maxwell's Equations as a Hyperbolic Conservative System / 9.1：
The Conservative Form of Maxwell's Equations / 9.1.1：
Characteristics and Wavefront Propagation / 9.1.2：
An Elementary Form of the Finite-Volume Method / 9.1.3：
Finite-Volume Discretization of Maxwell's Equations / 9.2：
Spatial Discretizations / 9.2.1：
Temporal Discretization / 9.2.2：
Consistency and Stability / 9.2.3：
Hybridization of the FVTD Method with Other Models and Methods / 9.3：
Thin-Wire Models in the FVTD Method / 9.3.1：
Hybridization of the FVTD and the FDTD Methods / 9.3.2：
Another Approach of the Finite-Volume Approach / 9.3.3：
Dielectric Structures / 9.4：
Thin Screens with Finite Conductivity / 9.4.2：
Thin Wires / 9.4.3：
Index / 9.5：
Preface
Acknowledgments
Contributors
16.

図書
図書
16. Elementary Lie group analysis and ordinary differential equations
Nail H. Ibragimov
出版情報: Chichester, West Sussex ; New York : Wiley, c1999  xviii, 347 p. ; 24 cm
シリーズ名: Mathematical methods in practice ; v. 4
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目次情報: 続きを見る
Introduction to Differential Equations
Transformation Groups
Lie Group Analysis of Ordinary Differential Equations
Brief on Lie Algebras
First Order Differential Equations
Integration of Second Order Equations
Basic Theory of Linear Equations
Nonlinear Second Order Equations
Integration of Third Order Equations
Nonlinear Superposition Principle
Index
Introduction to Differential Equations
Transformation Groups
Lie Group Analysis of Ordinary Differential Equations
17.

図書
図書
17. Numerical methods for bifurcation problems and large-scale dynamical systems
Eusebius Doedel, Laurette S. Tuckerman, editors
出版情報: New York : Springer, c2000  x, 471 p. ; 25 cm
シリーズ名: The IMA volumes in mathematics and its applications ; v. 119
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18.

図書
図書
18. Sobolev gradients and differential equations
J.W. Neuberger
出版情報: Berlin : Springer-Verlag, c1997  viii, 149 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1670
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19.

図書
図書
19. Transformations of manifolds and applications to differential equations
Keti Tenenblat
出版情報: Harlow : Longman, 1998  x, 209 p. ; 25 cm
シリーズ名: Pitman monographs and surveys in pure and applied mathematics ; 93
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Preface
Transformations of surfaces and applications / I：
Submanifolds of constant Sectional curvature / II：
Pseudo-spherical geodesic congruences and applications / III：
The generating equation / IV：
The generating intrinsic equation / V：
Laplace transformation in higher dimensions / VI：
References
Index
Preface
Transformations of surfaces and applications / I：
Submanifolds of constant Sectional curvature / II：
20.

図書
図書
20. Symmetries and conservation laws for differential equations of mathematical physics
A.V. Bocharov ... [et al.] ; I.S. Krasilʹshchik, A.M. Vinogradov (editor) ; [translated from the Russian by A.M. Verbovetsky and I.S. Krasilʹshchik]
出版情報: Providence, R.I. : American Mathematical Society, c1999  xiv, 333 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 182
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Ordinary differential equations
First-order equations
The theory of classical symmetries
Higher symmetries
Conservation laws
Nonlocal symmetries
From symmetries of partial differential equations towards secondary ("quantized") calculus
Bibliography
Index
Ordinary differential equations
First-order equations
The theory of classical symmetries
21.

図書
図書
21. Fractional analysis : methods of motion decomposition
Igor V. Novozhilov
出版情報: Boston : Birkhäuser, 1997  x, 231 p. ; 25 cm
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22.

図書
図書
22. Approximation methods for solutions of differential and integral equations
V.K. Dzyadyk
出版情報: Utrecht : VSP, 1995  325 p. ; 25 cm
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23.

図書
図書
23. Multiple scale and singular perturbation methods
J. Kevorkian, J.D. Cole
出版情報: New York ; Tokyo : Springer, c1996  viii, 632 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 114
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24.

図書
図書
24. Rigid local systems (: hc ; : pbk)
by Nicholas M. Katz
出版情報: Princeton, N.J. : Princeton University Press, 1996  vii, 223 p. ; 25 cm
シリーズ名: Annals of mathematics studies ; no. 139
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First results on rigid local systems
The theory of middle concolution
Fourier
Transform and rigidity
Middle concolution: dependence on parameters
Structure of rigid local systems
Existence algorithms for rigids
Diophantine aspects of rigidity rigids
First results on rigid local systems
The theory of middle concolution
Fourier
25.

図書
図書
25. New trends in theoretical developments and computational methods
edited by N.H. Ibragimov ... [et al.]
出版情報: Boca Raton, Fl. ; Tokyo : CRC Press, c1996  xvi, 536 p. ; 25 cm
シリーズ名: CRC handbook of Lie group analysis of differential equations / edited by N.H. Ibragimov ; v. 3
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26.

図書
図書
26. Handbook of exact solutions for ordinary differential equations
Andrei D. Polyanin, Valentin F. Zaitsev
出版情報: Boca Raton ; Tokyo : CRC Press, c1995  707 p. ; 27 cm
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27.

図書
図書
27. Nonstiff problems (: Berlin ; : New York)
E. Hairer, S.P. Nørsett, G. Wanner
出版情報: Berlin ; Tokyo : Springer-Verlag, c1987  xiii, 480 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 8 . Solving ordinary differential equations ; 1
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28.

図書
図書
28. Differential equations and numerical analysis (: pbk)
Andrew Paterson
出版情報: Cambridge : Cambridge University Press, 1991  x, 609 p. ; 23 cm
シリーズ名: SMP further mathematics series
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29.

図書
図書
29. Methods of solving singular systems of ordinary differential equations
Yuri Boyarintsev ; translated by Vassily Michalkowski
出版情報: Chichester : Wiley, c1992  vi, 163 p. ; 24 cm
シリーズ名: Pure and applied mathematics
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30.

図書
図書
30. Qualitative theory of differential equations
Zhang Zhi-fen ... [et al.] ; translated by Anthony Wing-Kwok Leung
出版情報: Providence, R.I. : American Mathematical Society, c1992  xiv, 461 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 101
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31.

図書
図書
31. 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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32.

図書
図書
32. Differential equations : their solution using symmetries (: pbk)
Hans Stephani ; edited by Malcolm MacCallum
出版情報: Cambridge [England] ; New York : Cambridge University Press, c1989  xii, 260 p. ; 24 cm
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目次情報: 続きを見る
Preface
Introduction / 1：
Ordinary differential equations / I：
Point transformations and their generators / 2：
One-parameter groups of point transformations and their infinitesimal generators / 2.1：
Transformation laws and normal forms of generators / 2.2：
Extensions of transformations and their generators / 2.3：
Multiple-parameter groups of transformations and their generators / 2.4：
Exercises / 2.5：
Lie point symmetries of ordinary differential equations: the basic definitions and properties / 3：
The definition of a symmetry: first formulation / 3.1：
Ordinary differential equations and linear partial differential equations of first order / 3.2：
The definition of a symmetry: second formulation / 3.3：
Summary / 3.4：
How to find the Lie point symmetries of an ordinary differential equation / 3.5：
Remarks on the general procedure / 4.1：
The atypical case: first order differential equations / 4.2：
Second order differential equations / 4.3：
Higher order differential equations. The general nth order linear equation / 4.4：
How to use Lie point symmetries: differential equations with one symmetry / 4.5：
First order differential equations / 5.1：
Higher order differential equations / 5.2：
Some basic properties of Lie algebras / 5.3：
The generators of multiple-parameter groups and their Lie algebras / 6.1：
Examples of Lie algebras / 6.2：
Subgroups and subalgebras / 6.3：
Realizations of Lie algebras. Invariants and differential invariants / 6.4：
Nth order differential equations with multiple-parameter symmetry groups: an outlook / 6.5：
How to use Lie point symmetries: second order differential equations admitting a G[subscript 2] / 6.6：
A classification of the possible subcases, and ways one might proceed / 7.1：
The first integration strategy: normal forms of generators in the space of variables / 7.2：
The second integration strategy: normal forms of generators in the space of first integrals / 7.3：
Summary: Recipe for the integration of second order differential equations admitting a group G[subscript 2] / 7.4：
Examples / 7.5：
Second order differential equations admitting more than two Lie point symmetries / 7.6：
The problem: groups that do not contain a G[subscript 2] / 8.1：
How to solve differential equations that admit a G[subscript 3] IX / 8.2：
Example / 8.3：
Higher order differential equations admitting more than one Lie point symmetry / 8.4：
The problem: some general remarks / 9.1：
First integration strategy: normal forms of generators in the space(s) of variables / 9.2：
Second integration strategy: normal forms of generators in the space of first integrals. Lie's theorem / 9.3：
Third integration strategy: differential invariants / 9.4：
Systems of second order differential equations / 9.5：
The corresponding linear partial differential equation of first order and the symmetry conditions / 10.1：
Example: the Kepler problem / 10.2：
Systems possessing a Lagrangian: symmetries and conservation laws / 10.3：
Symmetries more general than Lie point symmetries / 10.4：
Why generalize point transformations and symmetries? / 11.1：
How to generalize point transformations and symmetries / 11.2：
Contact transformations / 11.3：
How to find and use contact symmetries of an ordinary differential equation / 11.4：
Dynamical symmetries: the basic definitions and properties / 11.5：
What is a dynamical symmetry? / 12.1：
Examples of dynamical symmetries / 12.2：
The structure of the set of dynamical symmetries / 12.3：
How to find and use dynamical symmetries for systems possessing a Lagrangian / 12.4：
Dynamical symmetries and conservation laws / 13.1：
Example: L = (x[superscript 2] + y[superscript 2])/2 - a(2y[superscript 3] + x[superscript 2]y), a [characters not producible] 0 / 13.2：
Example: geodesics of a Riemannian space - Killing vectors and Killing tensors / 13.3：
Systems of first order differential equations with a fundamental system of solutions / 13.5：
The problem / 14.1：
The answer / 14.2：
Systems with a fundamental system of solutions and linear systems / 14.3：
Partial differential equations / 14.5：
Lie point transformations and symmetries / 15：
The definition of a symmetry / 15.1：
How to determine the point symmetries of partial differential equations / 15.4：
How to use Lie point symmetries of partial differential equations I: generating solutions by symmetry transformations / 16.1：
The structure of the set of symmetry generators / 17.1：
What can symmetry transformations be expected to achieve? / 17.2：
Generating solutions by finite symmetry transformations / 17.3：
Generating solutions (of linear differential equations) by applying the generators / 17.4：
How to use Lie point symmetries of partial differential equations II: similarity variables and reduction of the number of variables / 17.5：
Similarity variables and how to find them / 18.1：
Conditional symmetries / 18.3：
How to use Lie point symmetries of partial differential equations III: multiple reduction of variables and differential invariants / 18.5：
Multiple reduction of variables step by step / 19.1：
Multiple reduction of variables by using invariants / 19.2：
Some remarks on group-invariant solutions and their classification / 19.3：
Symmetries and the separability of partial differential equations / 19.4：
Some remarks on the usual separations of the wave equation / 20.1：
Hamilton's canonical equations and first integrals in involution / 20.3：
Quadratic first integrals in involution and the separability of the Hamilton-Jacobi equation and the wave equation / 20.4：
Contact transformations and contact symmetries of partial differential equations, and how to use them / 20.5：
The general contact transformation and its infinitesimal generator / 21.1：
Contact symmetries of partial differential equations and how to find them / 21.2：
Remarks on how to use contact symmetries for reduction of variables / 21.3：
Differential equations and symmetries in the language of forms / 21.4：
Vectors and forms / 22.1：
Exterior derivatives and Lie derivatives / 22.2：
Differential equations in the language of forms / 22.3：
Symmetries of differential equations in the language of forms / 22.4：
Lie-Backlund transformations / 22.5：
Why study more general transformations and symmetries? / 23.1：
Finite order generalizations do not exist / 23.2：
Lie-Backlund transformations and their infinitesimal generators / 23.3：
Examples of Lie-Backlund transformations / 23.4：
Lie-Backlund versus Backlund transformations / 23.5：
Lie-Backlund symmetries and how to find them / 23.6：
The basic definitions / 24.1：
Remarks on the structure of the set of Lie-Backlund symmetries / 24.2：
How to find Lie-Backlund symmetries: some general remarks / 24.3：
Examples of Lie-Backlund symmetries / 24.4：
Recursion operators / 24.5：
How to use Lie-Backlund symmetries / 24.6：
Similarity solutions for Lie-Backlund symmetries / 25.1：
Lie-Backlund symmetries and conservation laws / 25.3：
Lie-Backlund symmetries and generation methods / 25.4：
A short guide to the literature / 25.5：
Solutions to some of the more difficult exercises / Appendix B：
Index
Preface
Introduction / 1：
Ordinary differential equations / I：
33.

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図書
33. 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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34.

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34. 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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35.

図書
図書
35. 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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36.

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36. Differential equations with small parameters and relaxation oscillations
E.F. Mishchenko and N.Kh. Rozov ; translated from Russian by F.M.C. Goodspeed
出版情報: New York : Plenum Press, c1980  x, 228 p. ; 24 cm
シリーズ名: Mathematical concepts and methods in science and engineering ; 13
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37.

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37. Elementary stability and bifurcation theory. 2nd ed (: us ; : gw)
Gérard Iooss, Daniel D. Joseph
出版情報: New York ; Tokyo : Springer-Verlag, c1990  xxiii, 324 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Asymptotic Solutions of Evolution Problems
Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension
Imperfection Theory and Isolated Solutions Which Perturb Bifurcation
Stability of Steady Solutions of Evolution Equations in Two Dimensions and n Dimensions. Appendices
Bifurcation of Steady Solution in Two Dimensions and the Stability of the Bifurcating Solutions. Appendix
Methods of Projection for General Problems of Bifurcation into Steady Solutions
Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions
Bifurcation of Periodic Solutions in the General Case
Subharmonic Bifurcation of Forced T-Periodic Solutions
Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions. Appendices
Secondary Subharmonic and Symptotically Quasi-Periodic Bifurcation of Periodic Solutions (of Hopf's Type) in the Autonomous Case
Stability and Bifurcation in Conservative Systems
Asymptotic Solutions of Evolution Problems
Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension
Imperfection Theory and Isolated Solutions Which Perturb Bifurcation
38.

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図書
38. 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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39.

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図書
39. Global bifurcations and chaos : analytical methods (: us ; : gw ; : softcover)
Stephen Wiggins
出版情報: New York ; Berlin ; Tokyo : Springer-Verlag, c1988  xiv, 494 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 73
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目次情報: 続きを見る
Introduction: Background for Ordinary Differential Equations and Dynamical Systems
Chaos: Its Descriptions and Conditions for Existence
Homoclinic and Heteroclinic Motions
Global Pertubation Methods for Detecting Chaotic Dynamics
References
Index
Introduction: Background for Ordinary Differential Equations and Dynamical Systems
Chaos: Its Descriptions and Conditions for Existence
Homoclinic and Heteroclinic Motions
40.

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図書
40. 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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41.

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41. 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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42.

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42. Numerical solutions of differential equations
H. Levy and E.A. Baggott
出版情報: New York : Dover Publications, 1950  viii, 238 p. ; 21 cm.
シリーズ名: Dover books on advanced mathematics ; S168
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43.

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43. Direct methods (: Basel ; : Boston)
Aleksandr A. Samarskii, Evgenii S. Nikolaev ; translated from the Russian by Stephen G. Nash
出版情報: Basel [Switzerland] ; Boston : Birkhäuser, 1989  xxxv, 242 p. ; 24 cm
シリーズ名: Numerical methods for grid equations / Aleksandr A. Samarskii, Evgenii S. Nikolaev ; translated from the Russian by Stephen G. Nash ; v. 1
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44.

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44. Numerical methods for grid equations
Aleksandr A. Samarskii, Evgenii S. Nikolaev ; translated from the Russian by Stephen G. Nash
出版情報: Basel [Switzerland] ; Boston : Birkhäuser Verlag, 1989  2 v. ; 24 cm
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45.

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45. Iterative methods (: Basel ; : Boston)
Aleksandr A. Samarskii, Evgenii S. Nikolaev ; translated from the Russian by Stephen G. Nash
出版情報: Basel [Switzerland] ; Boston : Birkhäuser, 1989  xv, 502 p. ; 24 cm
シリーズ名: Numerical methods for grid equations / Aleksandr A. Samarskii, Evgenii S. Nikolaev ; translated from the Russian by Stephen G. Nash ; v. 2
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46.

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46. Variational methods in mathematics, science, and engineering. 2nd ed
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
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47.

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47. Symmetries and differential equations (: New York ; : Berlin)
George W. Bluman, Sukeyuki Kumei
出版情報: New York ; Tokyo : Springer-Verlag, c1989  xiii, 412 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 81
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48.

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48. Discrete variable methods in ordinary differential equations
Peter Henrici
出版情報: New York : Wiley, c1962  xi, 407 p. ; 24 cm
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49.

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49. 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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50.

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50. 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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