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1.

図書
図書
1. Methods of qualitative theory of differential equations and related topics (Supplement)
L. Lerman, G. Polotovskiĭ, L. Shilnikov, editors
出版情報: Providence, R.I. : American Mathematical Society, c2000  viii, 196 p. ; 26 cm
シリーズ名: American Mathematical Society translations ; ser. 2, v. 200 . Advances in the mathematical sciences (formerly advances in Soviet mathematics) ; 48
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Evgeniya Aleksandrovna Leontovich-Andronova (1905-1996) / L. P. Shilnikov
On the abundance of traveling waves in coupled expanding circle maps / V. Afraimovich ; M. Courbage
On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve / S. A. Alekseeva
Collapse and continuity of geodesic frameworks of surface foliations / S. Aranson ; V. Medvedev ; E. Zhuzhoma
Homoclinic and heteroclinic linkages in concrete systems: Nonlocal analysis and model maps / V. N. Belykh
On the mutual arrangement of a conic and a quintic in the real projective plane / A. A. Binstein ; G. M. Polotovskii
The structure of the boundary curve for planar controllability domains / N. N. Butenina
Orbit structure in a neighborhood of a separatrix cycle containing two saddle-foci / V. V. Bykov
Example of a blue sky catastrophe / N. Gavrilov ; A. Shilnikov
Dynamics and moduli of $\Omega$-conjugacy of 4D-diffeomorphisms with a structurally unstable homoclinic orbit to a saddle-focus fixed point / S. V. Gonchenko
Topological classification of amply situated attractors of $A$-diffeomorphisms of surfaces / V. Z. Grines ; R. V. Plykin
A proof of Shilnikov's theorem for $C^1$-smooth dynamical systems / M. V. Shashkov ; D. V. Turaev
A new simple bifurcation of a periodic orbit of "blue sky catastrophe" type
On the splitting of the complex loop of a separatrix / V. P. Tareev
Some topological structures of quadratic systems with at least four limit cycles / A. A. E.
Torus maps from weak coupling of strong resonances / J. Guckenheimer ; I. Khibnik
Isoenergetical structure of integrable Hamiltonian systems in an extended neighborhood of a simple singular point: Three degrees of freedom / L. M. Lerman
Evgeniya Aleksandrovna Leontovich-Andronova (1905-1996) / L. P. Shilnikov
On the abundance of traveling waves in coupled expanding circle maps / V. Afraimovich ; M. Courbage
On cusp-bifurcations of periodic orbits in systems with a saddle-focus homoclinic curve / S. A. Alekseeva
2.

図書
図書
2. Differential equations : linear, nonlinear, ordinary, partial (hbk. ; pbk.)
A.C. King, J. Billingham and S.R. Otto
出版情報: Cambridge : Cambridge University Press, c2003  xi, 541 p. ; 26 cm.
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Preface
Linear Equations / Part I：
Variable coefficient, second order, linear, ordinary differential equations / 1：
Legendre functions / 2：
Bessel functions / 3：
Boundary value problems, Green's functions and Sturm-Liouville theory / 4：
Fourier series and the Fourier transform / 5：
Laplace transforms / 6：
Classification, properties and complex variable methods for second order partial differential equations / 7：
Nonlinear Equations and Advanced Techniques / Part II：
Existence, uniqueness, continuity and comparison of solutions of ordinary differential equations / 8：
Nonlinear ordinary differential equations: phase plane methods / 9：
Group theoretical methods / 10：
Asymptotic methods: basic ideas / 11：
Asymptotic methods: differential equations / 12：
Stability, instability and bifurcations / 13：
Time-optimal control in the phase plane / 14：
An introduction to chaotic systems / 15：
Linear algebra / Appendix 1：
Continuity and differentiability / Appendix 2：
Power series / Appendix 3：
Sequences of functions / Appendix 4：
Ordinary differential equations / Appendix 5：
Complex variables / Appendix 6：
A short introduction to MATLAB / Appendix 7：
Bibliography
Index
Preface
Linear Equations / Part I：
Variable coefficient, second order, linear, ordinary differential equations / 1：
3.

図書
図書
3. Differential equations, dynamical systems, and an introduction to chaos. 2nd ed
Morris W. Hirsch, Stephen Smale, Robert L. Devaney
出版情報: San Diego ; Tokyo : Elsevier Academic Press, c2004  xiv, 417 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 60
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Preface
First-Order Equations / Chapter 1：
The Simplest Example / 1.1：
The Logistic Population Model / 1.2：
Constant Harvesting and Bifurcations / 1.3：
Periodic Harvesting and Periodic Solutions / 1.4：
Computing the Poincare Map / 1.5：
Exploration: A Two-Parameter Family / 1.6：
Planar Linear Systems / Chapter 2：
Second-Order Differential Equations / 2.1：
Planar Systems / 2.2：
Preliminaries from Algebra / 2.3：
Eigenvalues and Eigenvectors / 2.4：
Solving Linear Systems / 2.6：
The Linearity Principle / 2.7：
Phase Portraits for Planar Systems / Chapter 3：
Real Distinct Eigenvalues / 3.1：
Complex Eigenvalues / 3.2：
Repeated Eigenvalues / 3.3：
Changing Coordinates / 3.4：
Classification of Planar Systems / Chapter 4：
The Trace-Determinant Plane / 4.1：
Dynamical Classification / 4.2：
Exploration: A 3D Parameter Space / 4.3：
Higher Dimensional Linear Algebra / Chapter 5：
Preliminaries from Linear Algebra / 5.1：
Bases and Subspaces / 5.2：
Genericity / 5.5：
Higher Dimensional Linear Systems / Chapter 6：
Distinct Eigenvalues / 6.1：
Harmonic Oscillators / 6.2：
The Exponential of a Matrix / 6.3：
Nonautonomous Linear Systems / 6.5：
Nonlinear Systems / Chapter 7：
Dynamical Systems / 7.1：
The Existence and Uniqueness Theorem / 7.2：
Continuous Dependence of Solutions / 7.3：
The Variational Equation / 7.4：
Exploration: Numerical Methods / 7.5：
Equilibria in Nonlinear Systems / Chapter 8：
Some Illustrative Examples / 8.1：
Nonlinear Sinks and Sources / 8.2：
Saddles / 8.3：
Stability / 8.4：
Bifurcations / 8.5：
Exploration: Complex Vector Fields / 8.6：
Global Nonlinear Techniques / Chapter 9：
Nullclines / 9.1：
Stability of Equilibria / 9.2：
Gradient Systems / 9.3：
Hamiltonian Systems / 9.4：
Exploration: The Pendulum with Constant Forcing / 9.5：
Closed Orbits and Limit Sets / Chapter 10：
Limit Sets / 10.1：
Local Sections and Flow Boxes / 10.2：
The Poincare Map / 10.3：
Monotone Sequences in Planar Dynamical Systems / 10.4：
The Poincare-Bendixson Theorem / 10.5：
Applications of Poincare-Bendixson / 10.6：
Exploration: Chemical Reactions That Oscillate / 10.7：
Applications in Biology / Chapter 11：
Infectious Diseases / 11.1：
Predator/Prey Systems / 11.2：
Competitive Species / 11.3：
Exploration: Competition and Harvesting / 11.4：
Applications in Circuit Theory / Chapter 12：
An RLC Circuit / 12.1：
The Lienard Equation / 12.2：
The van der Pol Equation / 12.3：
A Hopf Bifurcation / 12.4：
Exploration: Neurodynamics / 12.5：
Applications in Mechanics / Chapter 13：
Newton's Second Law / 13.1：
Conservative Systems / 13.2：
Central Force Fields / 13.3：
The Newtonian Central Force System / 13.4：
Kepler's First Law / 13.5：
The Two-Body Problem / 13.6：
Blowing Up the Singularity / 13.7：
Exploration: Other Central Force Problems / 13.8：
Exploration: Classical Limits of Quantum Mechanical Systems / 13.9：
The Lorenz System / Chapter 14：
Introduction to the Lorenz System / 14.1：
Elementary Properties of the Lorenz System / 14.2：
The Lorenz Attractor / 14.3：
A Model for the Lorenz Attractor / 14.4：
The Chaotic Attractor / 14.5：
Exploration: The Rossler Attractor / 14.6：
Discrete Dynamical Systems / Chapter 15：
Introduction to Discrete Dynamical Systems / 15.1：
The Discrete Logistic Model / 15.2：
Chaos / 15.4：
Symbolic Dynamics / 15.5：
The Shift Map / 15.6：
The Cantor Middle-Thirds Set / 15.7：
Exploration: Cubic Chaos / 15.8：
Exploration: The Orbit Diagram / 15.9：
Homoclinic Phenomena / Chapter 16：
The Shil'nikov System / 16.1：
The Horseshoe Map / 16.2：
The Double Scroll Attractor / 16.3：
Homoclinic Bifurcations / 16.4：
Exploration: The Chua Circuit / 16.5：
Existence and Uniqueness Revisited / Chapter 17：
Proof of Existence and Uniqueness / 17.1：
Continuous Dependence on Initial Conditions / 17.3：
Extending Solutions / 17.4：
Nonautonomous Systems / 17.5：
Differentiability of the Flow / 17.6：
Bibliography
Index
Preface
First-Order Equations / Chapter 1：
The Simplest Example / 1.1：
4.

図書
図書
4. Nonlinear analysis and its applications to differential equations
M.R. Grossinho ... [et al.], editors
出版情報: Boston : Birkhäuser, c2001  xiii, 380 p. ; 25 cm
シリーズ名: Progress in nonlinear differential equations and their applications / editor, Haim Brezis ; 43
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5.

図書
図書
5. Differential equations & linear algebra. International ed.
C. Henry Edwards, David E. Penney
出版情報: Upper Saddle River, N.J. : Prentice Hall International, c2001  xiii, 684, 48, 6 p. ; 24 cm.
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First-Order Differential Equations / 1：
Differential Equations and Mathematical Model
Integrals as General and Particular Solutions
Direction Fields and Solution Curves
Separable Equations and Applications
Linear First-Order Equations
Substitution Methods and Exact Equations
Mathematical Models and Numerical Methods / 2：
Population Models
Equilibrium Solutions and Stability
Acceleration-Velocity Models
Numerical Approximation: Euler's Method
A Closer Look at the Euler Method
The Runge-Kutta Method
Linear Systems and Matrices / 3：
Introduction to Linear Systems
Matrices and Gaussian Elimination
Reduced Row-Echelon Matrices
Matrix Operations
Inverses of Matrices
Determinants
Linear Equations and Curve Fitting
Vector Spaces / 4：
The Vector Space R
The Vector Space Rn and Subspaces
Linear Combinations and Independence of Vectors
Bases and Dimension for Vector Spaces
General Vector Spaces
Linear Equations of Higher Order / 5：
Introduction: Second-Order Linear Equations
General Solutions of Linear Equations
Homogeneous Equations with Constant Coefficients
Mechanical Vibrations
Undetermined Coefficients and Variation of Parameters
Forced Oscillations and Resonance
Eigenvalues and Eigenvectors / 6：
Introduction to Eigenvalues
Diagonalization of Matrices
Applications Involving Powers of Matrices
Linear Systems of Differential Equations / 7：
First-Order Systems and Applications
Matrices and Linear Systems
The Eigenvalue Method for Linear Systems
Second-Order Systems and Mechanical Applications
Multiple Eigenvalue Solutions
Numerical Methods for Systems
Matrix Exponential Methods / 8：
Matrix Exponentials and Linear Systems
Nonhomogeneous Linear Systems
Spectral Decomposition Methods
Nonlinear Systems and Phenomena / 9：
Stability and the Phase Plane
Linear and Almost Linear Systems
Ecological Models: Predators and Competitors
Nonlinear Mechanical Systems
Laplace Transform Methods / 10：
Laplace Transforms and Inverse Transforms
Transformation of Initial Value Problems
Translation and Partial Fractions
Derivatives, Integrals, and Products of Transforms
Periodic and Piecewise Continuous Forcing Functions
Power Series Methods / 11：
Introduction and Review of Power Series
Power Series Solutions
Frobenius Series Solutions
Bessel's Equation
References for Further Study
The Existence and Uniqueness of Solutions / Appendix A：
Theory of Determinants / Appendix B：
Answers to Selected Problems
Index
First-Order Differential Equations / 1：
Differential Equations and Mathematical Model
Integrals as General and Particular Solutions
6.

図書
図書
6. Ordinary and partial differential equations : with special functions, Fourier series, and boundary value problems (: pbk)
Ravi P. Agarwal, Donal O'Regan
出版情報: New York ; London : Springer, c2009  xiv, 410 p. ; 24 cm
シリーズ名: Universitext
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Preface
Solvable Differential Equations / 1：
Second-Order Differential Equations / 2：
Preliminaries to Series Solutions / 3：
Solution at an Ordinary Point / 4：
Solution at a Singular Point / 5：
Solution at a Singular Point (Cont'd.) / 6：
Legendre Polynomials and Functions / 7：
Chebyshev, Hermite and Laguerre Polynomials / 8：
Bessel Functions / 9：
Hypergeometric Functions / 10：
Piecewise Continuous and Periodic Functions / 11：
Orthogonal Functions and Polynomials / 12：
Orthogonal Functions and Polynomials (Cont'd.) / 13：
Boundary Value Problems / 14：
Boundary Value Problems (Cont'd.) / 15：
Green's Functions / 16：
Regular Perturbations / 17：
Singular Perturbations / 18：
Sturm-Liouville Problems / 19：
Eigenfunction Expansions / 20：
Eigenfunction Expansions (Cont'd.) / 21：
Convergence of the Fourier Series / 22：
Convergence of the Fourier Series (Cont'd.) / 23：
Fourier Series Solutions of Ordinary Differential Equations / 24：
Partial Differential Equations / 25：
First-Order Partial Differential Equations / 26：
Solvable Partial Differential Equations / 27：
The Canonical Forms / 28：
The Method of Separation of Variables / 29：
The One-Dimensional Heat Equation / 30：
The One-Dimensional Heat Equation (Cont'd.) / 31：
The One-Dimensional Wave Equation / 32：
The One-Dimensional Wave Equation (Cont'd.) / 33：
Laplace Equation in Two Dimensions / 34：
Laplace Equation in Polar Coordinates / 35：
Two-Dimensional Heat Equation / 36：
Two-Dimensional Wave Equation / 37：
Laplace Equation in Three Dimensions / 38：
Laplace Equation in Three Dimensions (Cont'd.) / 39：
Nonhomogeneous Equations / 40：
Fourier Integral and Transforms / 41：
Fourier Integral and Transforms (Cont'd.) / 42：
Fourier Transform Method for Partial DEs / 43：
Fourier Transform Method for Partial DEs (Cont'd.) / 44：
Laplace Transforms / 45：
Laplace Transforms (Cont'd.) / 46：
Laplace Transform Method for Ordinary DEs / 47：
Laplace Transform Method for Partial DEs / 48：
Well-Posed Problems / 49：
Verification of Solutions / 50：
References for Further Reading
Index
Preface
Solvable Differential Equations / 1：
Second-Order Differential Equations / 2：
7.

図書
図書
7. Algebraic integrability, Painlevé geometry and Lie algebras
Mark Adler, Pierre van Moerbeke, Pol Vanhaecke
出版情報: Berlin : Springer, c2004  xii, 483 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, v. 47
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8.

図書
図書
8. Normal forms, bifurcations and finiteness problems in differential equations (: pb)
edited by Yulij Ilyashenko and Christiane Rousseau ; technical editor, Gert Sabidussi
出版情報: Dordrecht : Kluwer Academic, c2004  xxiv, 513 p. ; 25 cm
シリーズ名: NATO science series ; Series II . Mathematics, physics, and chemistry ; v. 137
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Preface
Key to group picture
Participants
Contributors
Relations between Abelian integrals and limit cycles / M. Caubergh ; R. Roussarie
Topics on singularities and bifurcations of vector fields / F. Dumortier ; P. de Maesschalck
Recent advances in the analysis of divergence and singularities / J. Ecalle
Local bifurcations of limit cycles, Abel equations and LiFnard systems / J.-P. Frantoise
Complexity of computations with Pfaffian and Noetherian functions / A. Gabrielov ; N. Vorobjov
Hamiltonian bifurcations and local analytic classification / V. Gelfreich
Confluence of singular points and Stokes phenomena / A. Glutsyuk
Bifurcations of relaxation oscillations / J. Guckenheimer
Selected topics in differential equations with real and complex time / Y. Ilyashenko
Growth rate of the number of periodic points / V.Yu. Kaloshin
Normal forms, bifurcations and finiteness properties of vector fields / C. Rousseau
Aspects of planar polynomial vector fields: global versus local, real versus complex, analytic versus algebraic and geometric / D. Schlomiuk
Index
Preface
Key to group picture
Participants
9.

図書
図書
9. Differential models : an introduction with Mathcad
Alexander Solodov, Valery Ochkov
出版情報: Berlin : Springer, c2005  xi, 232 p. ; 24 cm
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Differential Mathematical Models
Integrable Differential Equations
Dynamic Model of the System with Heat Engineering
Stiff Differential Equations
Heat Transfer near the Critical Point
The Faulkner-Skan Equation of Boundary Layer
The Rayleigh Equation: Hydronamic Instability
Kinematic Waves of Concentration in Ion-Exchange Filters
Kinematic Shock Waves
Numerical Modeling of the CPU-board Temperature Field
Temperature Waves
Differential Mathematical Models
Integrable Differential Equations
Dynamic Model of the System with Heat Engineering
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