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1.

図書

図書
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
2.

図書

図書
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
3.

図書

図書
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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4.

図書

図書
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:
5.

図書

図書
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
6.

図書

図書
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
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:
8.

図書

図書
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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9.

図書

図書
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
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