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1.

図書

図書
Ernst Hairer, Christian Lubich, Gerhard Wanner
出版情報: Berlin ; Tokyo : Springer, c2002  xiii, 515 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; v. 31
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2.

図書

図書
Y. Eliashberg, N. Mishachev
出版情報: Providence, R.I. : American Mathematical Society, c2002  xvii, 206 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 48
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目次情報: 続きを見る
Intrigue Holonomic approximation: Jets and holonomy
Thom transversality theorem Holonomic approximation
Applications Differential relations and Gromov's $h$-principle: Differential relations
Homotopy principle Open Diff $V$-invariant differential relations
Applications to closed manifolds
The homotopy principle in symplectic geometry: Symplectic and contact basics
Symplectic and contact structures on open manifolds
Symplectic and contact structures on closed manifolds
Embeddings into symplectic and contact manifolds
Microflexibility and holonomic $\mathcal{R}$-approximation
First applications of microflexibility
Microflexible $\mathfrak{U}$-invariant differential relations
Further applications to symplectic geometry
Convex integration: One-dimensional convex integration
Homotopy principle for ample differential relations
Directed immersions and embeddings
First order linear differential operators Nash-Kuiper theorem
Bibliography
Index
Intrigue Holonomic approximation: Jets and holonomy
Thom transversality theorem Holonomic approximation
Applications Differential relations and Gromov's $h$-principle: Differential relations
3.

図書

図書
Franz J. Vesely
出版情報: New York : Kluwer Academic/Plenum Publishers, c2001  xvi, 259 p. ; 26 cm
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The Three Pillars of Computational Physics / I:
Finite Differences / 1:
Interpolation Formulae / 1.1:
NGF Interpolation / 1.1.1:
NGB Interpolation / 1.1.2:
ST Interpolation / 1.1.3:
Difference Quotients / 1.2:
DNGF Formulae / 1.2.1:
DNGB Formulae / 1.2.2:
DST Formulae / 1.2.3:
Finite Differences in Two Dimensions / 1.3:
Sample Applications / 1.4:
Classical Point Mechanics / 1.4.1:
Diffusion and Thermal Conduction / 1.4.2:
Linear Algebra / 2:
Exact Methods / 2.1:
Gauss Elimination and Back Substitution / 2.1.1:
Simplifying Matrices: The Householder Transformation / 2.1.2:
LU Decomposition / 2.1.3:
Tridiagonal Matrices: Recursion Method / 2.1.4:
Iterative Methods / 2.2:
Jacobi Relaxation / 2.2.1:
Gauss-Seidel Relaxation (GSR) / 2.2.2:
Successive Over-Relaxation (SOR) / 2.2.3:
Alternating Direction Implicit Method (ADI) / 2.2.4:
Conjugate Gradient Method (CG) / 2.2.5:
Eigenvalues and Eigenvectors / 2.3:
Largest Eigenvalue and Related Eigenvector / 2.3.1:
Arbitrary Eigenvalue/-vector: Inverse Iteration / 2.3.2:
Potential Equation / 2.4:
Electronic Orbitals / 2.4.3:
Stochastics / 3:
Equidistributed Random Variates / 3.1:
Linear Congruential Generators / 3.1.1:
Shift Register Generators / 3.1.2:
Other Distributions / 3.2:
Fundamentals / 3.2.1:
Transformation Method / 3.2.2:
Generalized Transformation Method / 3.2.3:
Rejection Method / 3.2.4:
Multivariate Gaussian Distribution / 3.2.5:
Equidistribution in Orientation Space / 3.2.6:
Random Sequences / 3.3:
Markov Processes / 3.3.1:
Autoregressive Processes / 3.3.3:
Wiener-Levy Process / 3.3.4:
Markov Chains and the Monte Carlo method / 3.3.5:
Stochastic Optimization / 3.4:
Simulated Annealing / 3.4.1:
Genetic Algorithms / 3.4.2:
Everything Flows / II:
Ordinary Differential Equations / 4:
Initial Value Problems of First Order / 4.1:
Euler-Cauchy Algorithm / 4.1.1:
Stability and Accuracy of Difference Schemes / 4.1.2:
Explicit Methods / 4.1.3:
Implicit Methods / 4.1.4:
Predictor-Corrector Method / 4.1.5:
Runge-Kutta Method / 4.1.6:
Extrapolation Method / 4.1.7:
Initial Value Problems of Second Order / 4.2:
Verlet Method / 4.2.1:
Nordsieck Formulation of the PC Method / 4.2.2:
Symplectic Algorithms / 4.2.4:
Numerov's Method / 4.2.6:
Boundary Value Problems / 4.3:
Shooting Method / 4.3.1:
Relaxation Method / 4.3.2:
Partial Differential Equations / 5:
Initial Value Problems I (Hyperbolic) / 5.1:
FTCS Scheme; Stability Analysis / 5.1.1:
Lax Scheme / 5.1.2:
Leapfrog Scheme (LF) / 5.1.3:
Lax-Wendroff Scheme (LW) / 5.1.4:
Lax and Lax-Wendroff in Two Dimensions / 5.1.5:
Initial Value Problems II (Parabolic) / 5.2:
FTCS Scheme / 5.2.1:
Implicit Scheme of First Order / 5.2.2:
Crank-Nicholson Scheme (CN) / 5.2.3:
Dufort-Frankel Scheme (DF) / 5.2.4:
Boundary Value Problems: Elliptic DE / 5.3:
Relaxation and Multigrid Techniques / 5.3.1:
ADI Method for the Potential Equation / 5.3.2:
Fourier Transform Method (FT) / 5.3.3:
Cyclic Reduction (CR) / 5.3.4:
Anchors Aweigh / III:
Simulation and Statistical Mechanics / 6:
Model Systems of Statistical Mechanics / 6.1:
A Nutshellfull of Fluids and Solids / 6.1.1:
Tricks of the Trade / 6.1.2:
Monte Carlo Method / 6.2:
Molecular Dynamics Simulation / 6.3:
Hard Spheres / 6.3.1:
Continuous Potentials / 6.3.2:
Beyond Basic Molecular Dynamics / 6.3.3:
Evaluation of Simulation Experiments / 6.4:
Pair Correlation Function / 6.4.1:
Autocorrelation Functions / 6.4.2:
Particles and Fields / 6.5:
Ewald summation / 6.5.1:
Particle-Mesh Methods (PM and P3M) / 6.5.2:
Stochastic Dynamics / 6.6:
Quantum Mechanical Simulation / 7:
Diffusion Monte Carlo (DMC) / 7.1:
Path Integral Monte Carlo (PIMC) / 7.2:
Wave Packet Dynamics (WPD) / 7.3:
Density Functional Molecular Dynamics (DFMD) / 7.4:
Hydrodynamics / 8:
Compressible Flow without Viscosity / 8.1:
Explicit Eulerian Methods / 8.1.1:
Particle-in-Cell Method (PIC) / 8.1.2:
Smoothed Particle Hydrodynamics (SPH) / 8.1.3:
Incompressible Flow with Viscosity / 8.2:
Vorticity Method / 8.2.1:
Pressure Method / 8.2.2:
Free Surfaces: Marker-and-Cell Method (MAC) / 8.2.3:
Lattice Gas Models for Hydrodynamics / 8.3:
Lattice Gas Cellular Automata / 8.3.1:
The Lattice Boltzmann Method / 8.3.2:
Direct Simulation Monte Carlo / Bird method / 8.4:
Appendixes
Machine Errors / A:
Discrete Fourier Transformation / B:
Fast Fourier Transform (FFT) / B.1:
Bibliography
Index
The Three Pillars of Computational Physics / I:
Finite Differences / 1:
Interpolation Formulae / 1.1:
4.

図書

図書
by Maria do Rosário Grossinho and Stepan Agop Tersian
出版情報: Dordrecht : Kluwer Academic Publishers, c2001  xii, 269 p. ; 25 cm
シリーズ名: Nonconvex optimization and its applications ; v. 52
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5.

図書

図書
William Edmund Milne
出版情報: New York : Wiley, c1953  xi, 275 p. ; 24 cm
シリーズ名: Applied mathematics series
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6.

図書

図書
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
7.

図書

図書
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
8.

図書

図書
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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9.

図書

図書
von E. Kamke
出版情報: Leipzig : Akademische Verlagsgesellschaft, 1962  xii, 316 p ; 24 cm
シリーズ名: Mathematik und ihre Anwendungen in Physik und Technik ; Reihe A ; Bd. 7 . Differentialgleichungen ; 1
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10.

図書

図書
von E. Kamke
出版情報: Leipzig : Akademische Verlagsgesellschaft, 1962  xv, 255 p. ; 24 cm
シリーズ名: Mathematik und ihre Anwendungen in Physik und Technik ; Reihe A ; Bd. 7 . Differentialgleichungen ; 2
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11.

図書

図書
George Emanuel
出版情報: Boca Raton, FL : Chapman & Hall/CRC, 2001  220 p.
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目次情報: 続きを見る
Preface
Background / I:
Introduction / 1:
Continuous One-Parameter Groups-I / 2:
Group Concept / 2.1:
Infinitesimal Transformation / 2.2:
Global Group Equations / 2.3:
Problems / 2.4:
Method of Characteristics / 3:
Theory / 3.1:
Examples / 3.2:
Continuous One-Parameter Groups-II / 3.3:
Invariance / 4.1:
The Once-Extended Group / 4.2:
Higher-Order Extended Groups / 4.3:
Ordinary Differential Equations / 4.4:
First-Order ODEs / 5:
Invariance Under a One-Parameter Group / 5.1:
Canonical Coordinates / 5.2:
Special Procedures / 5.3:
Compendium / 5.4:
Higher-Order ODEs / 5.5:
Invariant Equations / 6.1:
Finding the Groups / 6.2:
System of First-Order ODEs / 6.3:
Second-Order ODEs / 6.4:
Classification of Two-Parameter Groups / 7.1:
Invariance and Canonical Coordinates / 7.2:
Appendices / 7.3:
Bibliography and References / A:
The Rotation Group / B:
Basic Relations / C:
Tables / D:
Answers to Selected Problems / E:
Preface
Background / I:
Introduction / 1:
12.

図書

図書
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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13.

図書

図書
Arieh Iserles
出版情報: Cambridge : Cambridge University Press, 2009  xviii, 459 p. ; 25 cm
シリーズ名: Cambridge texts in applied mathematics
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Preface to the second edition
Preface to the first edition
Flowchart of contents
Ordinary differential equations / I:
Euler's method and beyond / 1:
Ordinary differential equations and the Lipschitz condition / 1.1:
Euler's method / 1.2:
The trapezoidal rule / 1.3:
The theta method / 1.4:
Comments and bibliography
Exercises
Multistep methods / 2:
The Adams method / 2.1:
Order and convergence of multistep methods / 2.2:
Backward differentiation formulae / 2.3:
Runge-Kutta methods / 3:
Gaussian quadrature / 3.1:
Explicit Runge-Kutta schemes / 3.2:
Implicit Runge-Kutta schemes / 3.3:
Collocation and IRK methods / 3.4:
Stiff equations / 4:
What are stiff ODEs? / 4.1:
The linear stability domain and A-stability / 4.2:
A-stability of Runge-Kutta methods / 4.3:
A-stability of multistep methods / 4.4:
Geometric numerical integration / 5:
Between quality and quantity / 5.1:
Monotone equations and algebraic stability / 5.2:
From quadratic invariants to orthogonal flows / 5.3:
Hamiltonian systems / 5.4:
Error control / 6:
Numerical software vs. numerical mathematics / 6.1:
The Milne device / 6.2:
Embedded Runge-Kutta methods / 6.3:
Nonlinear algebraic systems / 7:
Functional iteration / 7.1:
The Newton-Raphson algorithm and its modification / 7.2:
Starting and stopping the iteration / 7.3:
The Poisson equation / II:
Finite difference schemes / 8:
Finite differences / 8.1:
The finite element method / 8.2:
Two-point boundary value problems / 9.1:
A synopsis of FEM theory / 9.2:
Spectral methods / 9.3:
Sparse matrices vs. small matrices / 10.1:
The algebra of Fourier expansions / 10.2:
The fast Fourier transform / 10.3:
Second-order elliptic PDEs / 10.4:
Chebyshev methods / 10.5:
Gaussian elimination for sparse linear equations / 11:
Banded systems / 11.1:
Graphs of matrices and perfect Cholesky factorization / 11.2:
Classical iterative methods for sparse linear equations / 12:
Linear one-step stationary schemes / 12.1:
Classical iterative methods / 12.2:
Convergence of successive over-relaxation / 12.3:
Multigrid techniques / 12.4:
In lieu of a justification / 13.1:
The basic multigrid technique / 13.2:
The full multigrid technique / 13.3:
Poisson by multigrid / 13.4:
Conjugate gradients / 14:
Steepest, but slow, descent / 14.1:
The method of conjugate gradients / 14.2:
Krylov subspaces and preconditioners / 14.3:
Poisson by conjugate gradients / 14.4:
Fast Poisson solvers / 15:
TST matrices and the Hockney method / 15.1:
Fast Poisson solver in a disc / 15.2:
Partial differential equations of evolution / III:
The diffusion equation / 16:
A simple numerical method / 16.1:
Order, stability and convergence / 16.2:
Numerical schemes for the diffusion equation / 16.3:
Stability analysis I: Eigenvalue techniques / 16.4:
Stability analysis II: Fourier techniques / 16.5:
Splitting / 16.6:
Hyperbolic equations / 17:
Why the advection equation? / 17.1:
Finite differences for the advection equation / 17.2:
The energy method / 17.3:
The wave equation / 17.4:
The Burgers equation / 17.5:
Appendix Bluffer's guide to useful mathematics
Linear algebra / A.1:
Vector spaces / A.1.1:
Matrices / A.1.2:
Inner products and norms / A.1.3:
Linear systems / A.1.4:
Eigenvalues and eigenvectors / A.1.5:
Bibliography
Analysis / A.2:
Introduction to functional analysis / A.2.1:
Approximation theory / A.2.2:
Index / A.2.3:
Preface to the second edition
Preface to the first edition
Flowchart of contents
14.

図書

図書
von E. Kamke
出版情報: Leipzig : Akademische Verlagsgesellschaft, 1967  xxvi, 668 p. ; 24 cm
シリーズ名: Mathematik und ihre Anwendungen in Physik und Technik ; Reihe A ; Bd. 18. Differentialgleichungen : Lösungsmethoden und Lösungen ; 1
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15.

図書

図書
Ole Christensen
出版情報: Boston : Birkhäuser, c2003  xx, 440 p ; 24 cm
シリーズ名: Applied and numerical harmonic analysis / series editor, John J. Benedetto
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目次情報: 続きを見る
Preface
Frames in Finite-dimensional Inner Product Spaces / 1:
Some basic facts about frames / 1.1:
Frame bounds and frame algorithms / 1.2:
Frames in C[superscript n] / 1.3:
The discrete Fourier transform / 1.4:
Pseudo-inverses and the singular value decomposition / 1.5:
Finite-dimensional function spaces / 1.6:
Exercises / 1.7:
Infinite-dimensional Vector Spaces and Sequences / 2:
Sequences / 2.1:
Banach spaces and Hilbert spaces / 2.2:
L[superscript 2] (R) and l[superscript 2] (N) / 2.3:
The Fourier transform / 2.4:
Operators on L[superscript 2] (R) / 2.5:
Bases / 2.6:
Bases in Banach spaces / 3.1:
Bessel sequences in Hilbert spaces / 3.2:
Bases and biorthogonal systems in H / 3.3:
Orthonormal bases / 3.4:
The Gram matrix / 3.5:
Riesz bases / 3.6:
Fourier series and Gabor bases / 3.7:
Wavelet bases / 3.8:
Bases and their Limitations / 3.9:
Gabor systems and the Balian-Low Theorem / 4.1:
Bases and wavelets / 4.2:
General shortcomings / 4.3:
Frames in Hilbert Spaces / 5:
Frames and their properties / 5.1:
Frame sequences / 5.2:
Frames and operators / 5.3:
Frames and bases / 5.4:
Characterization of frames / 5.5:
The dual frames / 5.6:
Tight frames / 5.7:
Continuous frames / 5.8:
Frames and signal processing / 5.9:
Frames versus Riesz Bases / 5.10:
Conditions for a frame being a Riesz basis / 6.1:
Riesz frames and near-Riesz bases / 6.2:
Frames containing a Riesz basis / 6.3:
A frame which does not contain a basis / 6.4:
A moment problem / 6.5:
Exercise / 6.6:
Frames of Translates / 7:
Sequences in R[superscript d] / 7.1:
Frames of translates / 7.2:
Frames of integer-translates / 7.3:
Irregular frames of translates / 7.4:
The sampling problem / 7.5:
Frames of exponentials / 7.6:
Gabor Frames in L[superscript 2] (R) / 7.7:
Continuous representations / 8.1:
Gabor frames / 8.2:
Necessary conditions / 8.3:
Sufficient conditions / 8.4:
The Wiener space W / 8.5:
Special functions / 8.6:
General shift-invariant systems / 8.7:
Selected Topics on Gabor Frames / 8.8:
Popular Gabor conditions / 9.1:
Representations of the Gabor frame operator and duality / 9.2:
The duals of a Gabor frame / 9.3:
The Zak transform / 9.4:
Tight Gabor frames / 9.5:
The lattice parameters / 9.6:
Irregular Gabor systems / 9.7:
Applications of Gabor frames / 9.8:
Wilson bases / 9.9:
Gabor Frames in l[superscript 2] (Z) / 9.10:
Translation and modulation on l[superscript 2] (Z) / 10.1:
Discrete Gabor systems through sampling / 10.2:
Gabor frames in C[superscript L] / 10.3:
Shift-invariant systems / 10.4:
Frames in l[superscript 2] (Z) and filter banks / 10.5:
General Wavelet Frames / 10.6:
The continuous wavelet transform / 11.1:
Sufficient and necessary conditions / 11.2:
Irregular wavelet frames / 11.3:
Oversampling of wavelet frames / 11.4:
Dyadic Wavelet Frames / 11.5:
Wavelet frames and their duals / 12.1:
Tight wavelet frames / 12.2:
Wavelet frame sets / 12.3:
Frames and multiresolution analysis / 12.4:
Frame Multiresolution Analysis / 12.5:
Frame multiresolution analysis / 13.1:
Relaxing the conditions / 13.2:
Construction of frames / 13.4:
Frames with two generators / 13.5:
Some limitations / 13.6:
Wavelet Frames via Extension Principles / 13.7:
The general setup / 14.1:
The unitary extension principle / 14.2:
Applications to B-splines I / 14.3:
The oblique extension principle / 14.4:
Fewer generators / 14.5:
Applications to B-splines II / 14.6:
Approximation orders / 14.7:
Construction of pairs of dual wavelet frames / 14.8:
Applications to B-splines III / 14.9:
Perturbation of Frames / 14.10:
A Paley-Wiener Theorem for frames / 15.1:
Compact perturbation / 15.2:
Perturbation of frame sequences / 15.3:
Perturbation of Gabor frames / 15.4:
Perturbation of wavelet frames / 15.5:
Perturbation of the Haar wavelet / 15.6:
Approximation of the Inverse Frame Operator / 15.7:
The first approach / 16.1:
A general method / 16.2:
Applications to Gabor frames / 16.3:
Integer oversampled Gabor frames / 16.4:
The finite section method / 16.5:
Expansions in Banach Spaces / 16.6:
Representations of locally compact groups / 17.1:
Feichtinger-Grochenig theory / 17.2:
Banach frames / 17.3:
p-frames / 17.4:
Gabor systems and wavelets in L[superscript p] (R) and related spaces / 17.5:
Appendix A / 17.6:
Normed vector spaces and inner product spaces / A.1:
Linear algebra / A.2:
Integration / A.3:
Some special normed vector spaces / A.4:
Operators on Banach spaces / A.5:
Operators on Hilbert spaces / A.6:
The pseudo-inverse / A.7:
Some special functions / A.8:
B-splines / A.9:
Notes / A.10:
List of symbols
References
Index
Preface
Frames in Finite-dimensional Inner Product Spaces / 1:
Some basic facts about frames / 1.1:
16.

図書

図書
Bhimsen K. Shivamoggi
出版情報: Boston : Birkhäuser, c2003  xiv, 354 p. ; 24 cm
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17.

図書

図書
Andrei D. Polyanin, Valentin F. Zaitsev
出版情報: Boca Raton ; London : Chapman & Hall/CRC, c2003  xxvi, 787 p. ; 27 cm
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Authors
Foreword
Notations and Some Remarks
Introduction: Some Definitions, Formulas, Methods, and Transformations
First-Order Differential Equations / 0.1.:
General Concepts. The Cauchy Problem. Uniqueness and Existence Theorems / 0.1.1.:
Equations Solved for the Derivative. Simplest Techniques of Integration / 0.1.2.:
Exact Differential Equations. Integrating Factor / 0.1.3.:
Riccati Equation / 0.1.4.:
Abel Equations of the First Kind / 0.1.5.:
Abel Equations of the Second Kind / 0.1.6.:
Equations Not Solved for the Derivative / 0.1.7.:
Contact Transformations / 0.1.8.:
Approximate Analytic Methods for Solution of Equations / 0.1.9.:
Numerical Integration of Differential Equations / 0.1.10.:
Second-Order Linear Differential Equations / 0.2.:
Formulas for the General Solution. Some Transformations / 0.2.1.:
Representation of Solutions as a Series in the Independent Variable / 0.2.2.:
Asymptotic Solutions / 0.2.3.:
Boundary Value Problems / 0.2.4.:
Eigenvalue Problems / 0.2.5.:
Second-Order Nonlinear Differential Equations / 0.3.:
Form of the General Solution. Cauchy Problem / 0.3.1.:
Equations Admitting Reduction of Order / 0.3.2.:
Methods of Regular Series Expansions with Respect to the Independent Variable or Small Parameter / 0.3.3.:
Perturbation Methods of Mechanics and Physics / 0.3.4.:
Galerkin Method and Its Modifications (Projection Methods) / 0.3.5.:
Iteration and Numerical Methods / 0.3.6.:
Linear Equations of Arbitrary Order / 0.4.:
Linear Equations with Constant Coefficients / 0.4.1.:
Linear Equations with Variable Coefficients / 0.4.2.:
Asymptotic Solutions of Linear Equations / 0.4.3.:
Nonlinear Equations of Arbitrary Order / 0.5.:
Structure of the General Solution. Cauchy Problem / 0.5.1.:
A Method for Construction of Solvable Equations of General Form / 0.5.2.:
Lie Group and Discrete-Group Methods / 0.6.:
Lie Group Method. Point Transformations / 0.6.1.:
Contact Transformations. Backlund Transformations. Formal Operators. Factorization Principle / 0.6.2.:
First Integrals (Conservation Laws) / 0.6.3.:
Discrete-Group Method. Point Transformations / 0.6.4.:
Discrete-Group Method. The Method of RF-Pairs / 0.6.5.:
Simplest Equations with Arbitrary Functions Integrable in Closed Form / 1.:
Equations of the Form y'[subscript x] = f(x) / 1.1.1.:
Equations of the Form y'[subscript x] = f(y) / 1.1.2.:
Separable Equations y'[subscript x] = f(x)g(y) / 1.1.3.:
Linear Equation g(x)y'[subscript x] = f[subscript 1](x)y + f[subscript 0](x) / 1.1.4.:
Bernoulli Equation g(x)y'[subscript x] = f[subscript 1](x)y + f[subscript n](x)y[superscript n] / 1.1.5.:
Homogeneous Equation y'[subscript x] = f(y/x) / 1.1.6.:
Riccati Equation g(x)y'[subscript x] = f[subscript 2](x)y[superscript 2] + f[subscript 1](x)y + f[subscript 0](x) / 1.2.:
Preliminary Remarks / 1.2.1.:
Equations Containing Power Functions / 1.2.2.:
Equations Containing Exponential Functions / 1.2.3.:
Equations Containing Hyperbolic Functions / 1.2.4.:
Equations Containing Logarithmic Functions / 1.2.5.:
Equations Containing Trigonometric Functions / 1.2.6.:
Equations Containing Inverse Trigonometric Functions / 1.2.7.:
Equations with Arbitrary Functions / 1.2.8.:
Some Transformations / 1.2.9.:
Equations of the Form yy'[subscript x] - y = f(x) / 1.3.:
Equations of the Form yy'[subscript x] = f(x)y + 1 / 1.3.2.:
Equations of the Form yy'[subscript x] = f[subscript 1](x)y + f[subscript 0](x) / 1.3.3.:
Equations of the Form [g[subscript 1](x)y + g[subscript 0](x)]y'[subscript x] = f[subscript 2](x)y[superscript 2] + f[subscript 1](x)y + f[subscript 0](x) / 1.3.4.:
Some Types of First- and Second-Order Equations Reducible to Abel Equations of the Second Kind / 1.3.5.:
Equations Containing Polynomial Functions of y / 1.4.:
Abel Equations of the First Kind y'[subscript x] = f[subscript 3](x)y[superscript 3] + f[subscript 2](x)y[superscript 2] + f[subscript 1](x)y + f[subscript 0](x) / 1.4.1.:
Equations of the Form (A[subscript 22]y[superscript 2] + A[subscript 12]xy + A[subscript 11]x[superscript 2] + A[subscript 0])y'[subscript x] = B[subscript 22]y[superscript 2] + B[subscript 12]xy + B[subscript 11]x[superscript 2] + B[subscript 0] / 1.4.2.:
Equations of the Form (A[subscript 22]y[superscript 2] + A[subscript 12]xy + A[subscript 11]x[superscript 2] + A[subscript 2]y + A[subscript 1]x)y'[subscript x] = B[subscript 22]y[superscript 2] + B[subscript 12]xy + B[subscript 11]x[superscript 2] + B[subscript 2]y + B[subscript 1]x / 1.4.3.:
Equations of the Form (A[subscript 22]y[superscript 2] + A[subscript 12]xy + A[subscript 11]x[superscript 2] + A[subscript 2]y + A[subscript 1]x + A[subscript 0])y'[subscript x] = B[subscript 22]y[superscript 2] + B[subscript 12]xy + B[subscript 11]x[superscript 2] + B[subscript 2]y + B[subscript 1]x + B[subscript 0] / 1.4.4.:
Equations of the Form (A[subscript 3]y[superscript 3] + A[subscript 2]xy[superscript 2] + A[subscript 1]x[superscript 2]y + A[subscript 0]x[superscript 3] + a[subscript 1]y + a[subscript 0]x)y'[subscript x] = B[subscript 3]y[superscript 3] + B[subscript 2]xy[superscript 2] + B[subscript 1]x[superscript 2]y + B[subscript 0]x[superscript 3] + b[subscript 1]y + b[subscript 0]x / 1.4.5.:
Equations of the Form f(x, y)y'[subscript x] = g(x, y) Containing Arbitrary Parameters / 1.5.:
Equations Containing Combinations of Exponential, Hyperbolic, Logarithmic, and Trigonometric Functions / 1.5.1.:
Equations of the Form F(x, y, y'[subscript x]) = 0 Containing Arbitrary Parameters / 1.6.:
Equations of the Second Degree in y'[subscript x] / 1.6.1.:
Equations of the Third Degree in y'[subscript x] / 1.6.2.:
Equations of the Form (y'[subscript x])[superscript k] = f(y) + g(x) / 1.6.3.:
Other Equations / 1.6.4.:
Equations of the Form f(x, y)y'[subscript x] = g(x, y) Containing Arbitrary Functions / 1.7.:
Equations Containing Exponential and Hyperbolic Functions / 1.7.1.:
Equations Containing Combinations of Exponential, Logarithmic, and Trigonometric Functions / 1.7.3.:
Equations of the Form F(x, y, y'[subscript x]) = 0 Containing Arbitrary Functions / 1.8.:
Some Equations / 1.8.1.:
Second-Order Differential Equations / 1.8.2.:
Linear Equations / 2.1.:
Representation of the General Solution Through a Particular Solution / 2.1.1.:
Equations Containing Combinations of Exponential, Logarithmic, Trigonometric, and Other Functions / 2.1.2.:
Autonomous Equations y"[subscript x x] = F(y, y'[subscript x]) / 2.1.9.:
Equations of the Form y"[subscript x x] - y'[subscript x] = f(y) / 2.2.1.:
Equations of the Form y"[subscript x x] + f(y)y'[subscript x] + y = 0 / 2.2.2.:
Lienard Equations y"[subscript x x] + f(y)y'[subscript x] + g(y) = 0 / 2.2.3.:
Rayleigh Equations y"[subscript x x] + f(y'[subscript x]) + g(y) = 0 / 2.2.4.:
Emden-Fowler Equation y"[subscript x x] = Ax[superscript n]y[superscript m] / 2.3.:
Exact Solutions / 2.3.1.:
Some Formulas and Transformations / 2.3.2.:
Equations of the Form y"[subscript x x] = A[subscript 1]x[superscript n[subscript 1]y[superscript m[subscript 1] + A[subscript 2]x[superscript n[subscript 2]y[superscript m[subscript 2] / 2.4.:
Classification Table / 2.4.1.:
Generalized Emden-Fowler Equation y"[subscript x x] = Ax[superscript n]y[superscript m](y'[subscript x])[superscript l] / 2.4.2.:
Equations of the Form y"[subscript x x] = A[subscript 1]x[superscript n[subscript 1]y[superscript m[subscript 1](y'[subscript x])[superscript l[subscript 1] + A[subscript 2]x[superscript n[subscript 2]y[superscript m[subscript 2](y'[subscript x])[superscript l[subscript 2] / 2.5.1.:
Modified Emden-Fowler Equation y"[subscript x x] = A[subscript 1]x[superscript -1]y'[subscript x] + A[subscript 2]x[superscript n]y[superscript m] / 2.6.1.:
Equations of the Form y"[subscript x x] = (A[subscript 1]x[superscript n[subscript 1]y[superscript m[subscript 1] + A[subscript 2]x[superscript n[subscript 2]y[superscript m[subscript 2])(y'[subscript x])[superscript l] / 2.6.2.:
Equations of the Form y"[subscript x x] = [sigma] Ax[superscript n]y[superscript m](y'[subscript x])[superscript l] + Ax[superscript n-1]y[superscript m+1](y'[subscript x])[superscript l-1] / 2.6.3.:
Other Equations (l[subscript 1] [not equal] l[subscript 2]) / 2.6.4.:
Equations of the Form y"[subscript x x] = f(x)g(y)h(y'[subscript x]) / 2.7.:
Equations of the Form y"[subscript x x] = f(x)g(y) / 2.7.1.:
Equations Containing Power Functions (h [characters not reproducible] const) / 2.7.2.:
Equations Containing Exponential Functions (h [characters not reproducible] const) / 2.7.3.:
Equations Containing Hyperbolic Functions (h [characters not reproducible] const) / 2.7.4.:
Equations Containing Trigonometric Functions (h [characters not reproducible] const) / 2.7.5.:
Some Nonlinear Equations with Arbitrary Parameters / 2.7.6.:
Painleve Transcendents / 2.8.1.:
Equations Containing the Combinations of Exponential, Hyperbolic, Logarithmic, and Trigonometric Functions / 2.8.3.:
Equations Containing Arbitrary Functions / 2.9.:
Equations of the Form F(x, y)y"[subscript xx] + G(x, y) = 0 / 2.9.1.:
Equations of the Form F(x, y)y"[subscript xx] + G(x, y)y'[subscript x] + H(x, y) = 0 / 2.9.2.:
Equations of the Form F(x, y)y"[subscript xx] + [characters not reproducible] G[subscript m](x, y)(y'[subscript x])[superscript m] = 0 (M = 2, 3, 4) / 2.9.3.:
Equations of the Form F(x, y, y'[subscript x])y"[subscript xx] + G(x, y, y'[subscript x]) = 0 / 2.9.4.:
Equations Not Solved for Second Derivative / 2.9.5.:
Equations of General Form / 2.9.6.:
Third-Order Differential Equations / 2.9.7.:
Equations of the Form y'"[subscript xxx] = Ax[superscript [alpha]y[superscript [beta](y'[subscript x])[superscript gamma](y"[subscript xx])[superscript [delta ] / 3.1.:
Equations of the Form y'"[subscript xxx] = Ay[superscript beta] / 3.2.1.:
Equations of the Form y'''[subscript xxx] = Ax[superscript alpha]y[superscript beta] / 3.2.3.:
Equations with |[gamma]| + |[delta]| [not equal] 0 / 3.2.4.:
Equations of the Form y'''[subscript xxx] = f(y)g(y'[subscript x])h(y''[subscript xx]) / 3.2.5.:
Nonlinear Equations with Arbitrary Parameters / 3.3.1.:
Nonlinear Equations Containing Arbitrary Functions / 3.4.1.:
Equations of the Form F(x, y)y'''[subscript xxx] + G(x, y) = 0 / 3.5.1.:
Equations of the Form F(x, y, y'[subscript x])y'''[subscript xxx] + G(x, y, y'[subscript x]) = 0 / 3.5.2.:
Equations of the Form F(x, y, y'[subscript x])y'''[subscript xxx] + G(x, y, y'[subscript x])y''[subscript xx] + H(x, y, y'[subscript x]) = 0 / 3.5.3.:
Equations of the Form F(x, y, y'[subscript x])y'''[subscript xxx] + [characters not reproducible]G[subscript alpha](x, y, y'[subscript x])(y''[subscript xx])[superscript alpha] = 0 / 3.5.4.:
Fourth-Order Differential Equations / 3.5.5.:
Nonlinear Equations / 4.1.:
Higher-Order Differential Equations / 4.2.1.:
Supplements / 5.1.:
Elementary Functions and Their Properties / S.1.:
Trigonometric Functions / S.1.1.:
Hyperbolic Functions / S.1.2.:
Inverse Trigonometric Functions / S.1.3.:
Inverse Hyperbolic Functions / S.1.4.:
Special Functions and Their Properties / S.2.:
Some Symbols and Coefficients / S.2.1.:
Error Functions and Exponential Integral / S.2.2.:
Gamma and Beta Functions / S.2.3.:
Incomplete Gamma and Beta Functions / S.2.4.:
Bessel Functions / S.2.5.:
Modified Bessel Functions / S.2.6.:
Degenerate Hypergeometric Functions / S.2.7.:
Hypergeometric Functions / S.2.8.:
Legendre Functions and Legendre Polynomials / S.2.9.:
Parabolic Cylinder Functions / S.2.10.:
Orthogonal Polynomials / S.2.11.:
The Weierstrass Function / S.2.12.:
Tables of Indefinite Integrals / S.3.:
Integrals Containing Rational Functions / S.3.1.:
Integrals Containing Irrational Functions / S.3.2.:
Integrals Containing Exponential Functions / S.3.3.:
Integrals Containing Hyperbolic Functions / S.3.4.:
Integrals Containing Logarithmic Functions / S.3.5.:
Integrals Containing Trigonometric Functions / S.3.6.:
Integrals Containing Inverse Trigonometric Functions / S.3.7.:
References
Index
Authors
Foreword
Notations and Some Remarks
18.

図書

図書
J.C. Butcher
出版情報: Chichester : Wiley, c2003  xiv, 425 p. ; 24 cm
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目次情報: 続きを見る
Preface
Differential and Difference Equations / 1:
Differential Equation Problems / 10:
Differential Equation Theory / 11:
Difference Equation Problems / 100:
Introduction to differential equations
Difference Equation Theory / 13:
The Kepler problem / 2:
Numerical Differential Equation Methods
The Euler Method / 102:
Many-body gravitational problems
Analysis of the Euler Method / 21:
A problem arising from the method of lines / 22:
Generalizations of the Euler Method
Runge-Kutta Methods / 104:
The simple pendulum
Linear Multistep Methods / 24:
A chemical kinetics problem / 25:
Taylor Series Methods
Hybrid Methods / 106:
The van der Pol equation and limit cycles
The Lotka-Volterra problem and periodic orbits / 3:
Preliminaries
Order Conditions / 31:
Low Order Explicit Methods / 32:
Existence and uniqueness of solutions / 33:
Runge-Kutta Methods with Error Estimates
Implicit Runge-Kutta Methods / 111:
Linear systems of differential equations
Stability of Implicit Runge-Kutta Methods / 35:
Stiff differential equations / 36:
Implementable Implicit Runge-Kutta Methods
Order Barriers / 113:
Laplace transforms
Algebraic Properties of Runge-Kutta Methods / 38:
Implementation Issues / 39:
Introduction to difference equations / 120:
A linear problem / 40:
The Order of Linear Multistep Methods
Errors and Error Growth / 122:
The Fibonacci difference equation
Stability Characteristics / 43:
Three quadratic problems / 44:
Order and Stability Barriers
One-leg Methods and G-stability / 124:
Iterative solutions of a polynomial equation
The arithmetic-geometric mean / 46:
General Linear Methods
Representing Methods in General Linear Form / 50:
Consistency, Stability and Convergence / 51:
Linear difference equations / 52:
The Stability of General Linear Methods
The Order of General Linear Methods / 131:
Constant coefficients
Methods with Runge-Kutta Stabiulity / 54:
References
Powers of matrices
Index
The Z-transform / 133:
Introduction to the Euler method / 200:
Some numerical experiments / 201:
Calculations with stepsize control / 202:
Calculations with mildly stiff problems / 203:
Calculations with the implicit Euler method / 204:
Formulation of the Euler method / 210:
Local truncation error / 211:
Global truncation error / 212:
Convergence of the Euler method / 213:
Order of convergence / 214:
Asymptotic error formula / 215:
Stability characteristics / 216:
Local truncation error estimation / 217:
Rounding error / 218:
Introduction / 220:
More computations in a step / 221:
Greater dependence on previous values / 222:
Use of higher derivatives / 223:
Multistep-multistage-multiderivative methods / 224:
Implicit methods / 225:
Local error estimates / 226:
Historical introduction / 230:
Second order methods / 231:
The coefficient tableau / 232:
Third order methods / 233:
Introduction to order conditions / 234:
Fourth order methods / 235:
Higher orders / 236:
Implicit Runge-Kutta methods / 237:
Numerical examples / 238:
Adams methods / 240:
General form of linear multistep methods / 242:
Consistency, stability and convergence / 243:
Predictor-corrector Adams methods / 244:
The Milne device / 245:
Starting methods / 246:
Introduction to Taylor series methods / 247:
Manipulation of power series / 251:
An example of a Taylor series solution / 252:
Other methods using higher derivatives / 253:
The use of f derivatives / 254:
Further numerical examples / 255:
Pseudo Runge-Kutta methods / 260:
Generalized linear multistep methods / 262:
General linear methods / 263:
Rooted trees / 264:
Functions on trees / 301:
Some combinatorial questions / 302:
The use of labelled trees / 303:
Differentiation / 304:
Taylor's theorem / 305:
Elementary differentials / 310:
The Taylor expansion of the exact solution / 311:
Elementary weights / 312:
The Taylor expansion of the approximate solution / 313:
Independence of the elementary differentials / 314:
Conditions for order / 315:
Order conditions for scalar problems / 316:
Independence of elementary weights / 317:
Methods of orders less than four / 318:
Simplifying assumptions / 321:
Methods of order four / 322:
New methods from old / 323:
Methods of order five / 324:
Methods of order six / 325:
Methods of orders greater than six / 326:
Richardson error estimates / 330:
Methods with built-in estimates / 332:
A class of error-estimating methods / 333:
The methods of Fehlberg / 334:
The methods of Verner / 335:
The methods of Dormand and Prince / 336:
Solvability of implicit equations / 340:
Methods based on Gaussian quadrature / 342:
Reflected methods / 343:
Methods based on Radau and Lobatto quadrature / 344:
A-stability, A([alpha])-stability and L-stability / 350:
Criteria for A-stability / 351:
Pade approximations to the exponential function / 352:
A-stability of Gauss and related methods / 353:
Order stars / 354:
Order arrows and the Ehle barrier / 355:
AN-stability / 356:
Non-linear stability / 357:
BN-stability of collocation methods / 358:
The V and W transformations / 359:
Implementation of implicit Runge-Kutta methods / 360:
Diagonally-implicit Runge-Kutta methods / 361:
The importance of high stage order / 362:
Singly implicit methods / 363:
Generalizations of singly-implicit methods / 364:
Effective order and DESIRE methods / 365:
Explicit barriers / 370:
An upper bound on the required number of stages / 371:
Motivation / 380:
Equivalence classes of Runge-Kutta methods / 381:
The group of Runge-Kutta methods / 382:
The Runge-Kutta group / 383:
A homomorphism between two groups / 384:
A generalization of G[subscript 1] / 385:
Recursive formula for the product / 386:
Some special elements of G / 387:
Some subgroups and quotient groups / 388:
An algebraic interpretation of effective order / 389:
Optimal sequences / 390:
Acceptance and rejection of steps / 392:
Error per step versus error per unit step / 393:
Control theoretic considerations / 394:
Solving the implicit equations / 395:
Fundamentals / 400:
Convergence / 401:
Stability / 403:
Consistency / 404:
Necessity of conditions for convergence / 405:
Sufficiency of conditions for convergence / 406:
Criteria for order / 410:
Derivation of methods / 411:
Backward difference methods / 412:
Further remarks on error growth / 420:
The underlying one-step method / 422:
Weakly stable methods / 423:
Variable stepsize / 424:
Stability regions / 430:
Examples of the boundary locus method / 432:
Examples of the Schur criterion / 433:
Stability of predictor-corrector methods / 434:
Survey of barrier results / 440:
Maximum order for a convergent k step method / 441:
Order stars for linear multistep methods / 442:
Order arrows for linear multistep methods / 443:
The one-leg counterpart to a linear multistep method / 450:
The concept of G-stability / 451:
Transformations relating one-leg and linear multistep methods / 452:
Effective order interpretation / 453:
Concluding remarks on G-stability / 454:
Survey of implementation considerations / 460:
Representation of data / 461:
Variable stepsize for Nordsieck methods / 462:
Local error estimation / 463:
Multivalue multistage methods / 500:
Transformations of methods / 501:
Runge-Kutta methods as general linear methods / 502:
Linear multistep methods as general linear methods / 503:
Some known unconventional methods / 504:
Some recently discovered general linear methods / 505:
Definitions of consistency and stability / 510:
Covariance of methods / 511:
Definition of convergence / 512:
The necessity of stability / 513:
The necessity of consistency / 514:
Stability and consistency imply convergence / 515:
Methods with maximal stability order / 520:
Possible definitions of order / 530:
Algebraic analysis of order / 531:
An example of the algebraic approach to order / 532:
Methods with Runge-Kutta stability / 533:
Design criteria for general linear methods / 540:
The types of DIMSIM methods / 541:
Runge-Kutta stability / 542:
Almost Runge-Kutta methods / 543:
Fourth order, four stage ARK methods / 544:
Doubly companion matrices / 545:
Inherent Runge-Kutta stability / 546:
Derivation of methods with IRK stability / 547:
Some nonstiff methods / 548:
Some stiff methods / 549:
Preface
Differential and Difference Equations / 1:
Differential Equation Problems / 10:
19.

図書

図書
by V.K. Andreev ... [et al.]
出版情報: Boston, Mass : Kluwer Academic, c1998  xii, 396 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 450
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20.

図書

図書
by Ravi P. Agarwal, Donal O'Regan and Patricia J.Y. Wong
出版情報: Dordrecht ; Boston, Mass. : Kluwer Academic Publishers, c1999  xi, 416 p. ; 25 cm
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21.

図書

図書
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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目次情報: 続きを見る
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
22.

図書

図書
Donald R. Smith
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1985  xvi, 500 p. ; 24 cm
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目次情報: 続きを見る
Preface
Acknowledgments
Preliminary results
Initial-Value Problems of Oscillatory Type / Part I:
Precession of the planet Mercury / 1:
Krylov/Bogoliubov averaging / 2:
The multiscale technique / 3:
Error estimates for perturbed-oscillation problems / 4:
Initial-Value Problems of Overdamped Type / Part II:
Linear overdamped initial-value problems / 5:
Nonlinear overdamped initial-value problems / 6:
Conditionally stable problems / 7:
Boundary-Value Problems / Part III:
Linear scalar problems / 8:
Linear first-order systems / 9:
Nonlinear problems / 10:
References
Name index
Subject index
Preface
Acknowledgments
Preliminary results
23.

図書

図書
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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24.

図書

図書
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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25.

図書

図書
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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26.

図書

図書
Ali Hasan Nayfeh
出版情報: New York : Wiley, c1981  xiv, 519 p. ; 24 cm
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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
27.

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
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28.

図書

図書
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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29.

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
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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.:
30.

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図書
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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図書

図書
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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32.

図書

図書
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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33.

図書

図書
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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34.

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
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35.

図書

図書
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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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
36.

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図書
L. Fox and D.F. Mayers
出版情報: London ; New York : Chapman and Hall, 1987  xi, 249 p. ; 24 cm
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37.

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図書
Igor V. Novozhilov
出版情報: Boston : Birkhäuser, 1997  x, 231 p. ; 25 cm
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38.

図書

図書
Andrei D. Polyanin, Valentin F. Zaitsev
出版情報: Boca Raton ; Tokyo : CRC Press, c1995  707 p. ; 27 cm
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39.

図書

図書
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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40.

図書

図書
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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目次情報: 続きを見る
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
41.

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図書
V.K. Dzyadyk
出版情報: Utrecht : VSP, 1995  325 p. ; 25 cm
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42.

図書

図書
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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43.

図書

図書
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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44.

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図書
J.R. Acton and P.T. Squire
出版情報: Bristol ; Boston : A. Hilger, c1985  x, 219 p. ; 24 cm
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45.

図書

図書
von E. Kamke
出版情報: New York : Chelsea Pub. Co., 1944  xxvi, 666 p. ; 24 cm
シリーズ名: Differentialgleichungen : Lösungsmethoden und Lösungen / von E. Kamke ; 1
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46.

図書

図書
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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47.

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図書
par F. Ceschino [et] J. Kuntzmann
出版情報: Paris : Dunod, 1963  xviii, 372 p ; 25 cm
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48.

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図書
Sasun Yakubov
出版情報: Essex, England : Longman Scientific & Technical , New York : John Wiley & Sons, 1994  245 p. ; 24 cm
シリーズ名: Pitman monographs and surveys in pure and applied mathematics ; 71
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49.

図書

図書
Robert Hermann
出版情報: Brookline, Mass. : Math Sci Press, c1994  286 p. ; 24 cm
シリーズ名: Interdisciplinary mathematics ; v. 29
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50.

図書

図書
edited by N.H. Ibragimov ... [et al.]
出版情報: Boca Raton, Fl. ; Tokyo : CRC Press, c1995  xix, 546 p. ; 25 cm
シリーズ名: CRC handbook of Lie group analysis of differential equations / edited by N.H. Ibragimov ; v. 2
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51.

図書

図書
Frank Stenger
出版情報: New York : Springer-Verlag, c1993  xv, 565 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 20
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52.

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
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53.

図書

図書
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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54.

図書

図書
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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55.

図書

図書
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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56.

図書

図書
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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57.

図書

図書
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
58.

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図書
von E. Kamke
出版情報: New York : Chelsea Pub. Co., 1944-74  2 v ; 24 cm
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目次情報:
Bd. 1. Gewöhnliche Differentialgleichungen. 3. Aufl
[Bd.] 2. Partielle Differentialgleichungen erster Ordnung für eine gesuchte Funktion
Bd. 1. Gewöhnliche Differentialgleichungen. 3. Aufl
[Bd.] 2. Partielle Differentialgleichungen erster Ordnung für eine gesuchte Funktion
59.

図書

図書
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
60.

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図書
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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61.

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図書
edited by G. Hall and J. M. Watt
出版情報: Oxford : Clarendon Press, 1976  336 p. ; 25 cm
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62.

図書

図書
Peter Henrici
出版情報: New York : Wiley, c1962  xi, 407 p. ; 24 cm
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63.

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図書
[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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64.

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図書
edited by Calvin H. Wilcox
出版情報: New York : Wiley, c1964  x, 249 p. ; 24 cm
シリーズ名: Publication ... of the Mathematics Research Center, United States Army, the University of Wisconsin ; no. 13
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65.

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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
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66.

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図書
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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67.

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図書
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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68.

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図書
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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69.

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図書
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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70.

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図書
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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71.

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図書
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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72.

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図書
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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73.

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図書
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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74.

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図書
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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75.

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図書
[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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76.

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図書
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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77.

図書

図書
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:
78.

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図書
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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79.

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図書
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
80.

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図書
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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目次情報: 続きを見る
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:
81.

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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
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82.

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図書
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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83.

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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
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84.

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図書
Miklós Farkas
出版情報: New York : Springer-Verlag, c1994  xiii, 577 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 104
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85.

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図書
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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86.

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図書
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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87.

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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
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