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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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目次情報: 続きを見る
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:
2.

図書

図書
Morris W. Hirsch and Stephen Smale
出版情報: New York : Academic Press, c1974  xi, 358 p. ; 23 cm
シリーズ名: Pure and applied mathematics ; v. 60
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目次情報: 続きを見る
Preface
First Examples
Newton's Equation and Kepler's Law
Linear Systems with Constant Coeffecients and Real Eigenvalues
Linear Systems with Constant Coefficients and Complex Eigenvalues
Linear Systems and Exponentials of Operators
Linear Systems and Canonical Forms of Operators
Contractions and Generic Properties of Operators
Fundamental Theory
Stability of Equilibria
Differential Equations for Electrical Circuits
The Poincare-Bendixson Theorem
Ecology
Periodic Attractors
Classical Mechanics
Nonautonomous Equations and Differentiability of Flows
Perturbation Theory and Structural Stability
Elementary Facts
Polynomials
On Canonical Forms
The Inverse Function Theorem
References
Answers to Selected Problems
Index
Preface
First Examples
Newton's Equation and Kepler's Law
3.

図書

図書
[by] Richard E. Williamson [and] Hale F. Trotter
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, [1974]  ix, 630 p. ; 25 cm
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目次情報:
04104-08 Trade Math One (20 Hours)
Builds on trainees' basic math skills to solve trade-reproblems
Covers calculations using denomiand volume calculations, English-metric system conversbasic geometry, and calculation of stretchouts
04104-08 Trade Math One (20 Hours)
Builds on trainees' basic math skills to solve trade-reproblems
Covers calculations using denomiand volume calculations, English-metric system conversbasic geometry, and calculation of stretchouts
4.

図書

図書
[by] Richard C. MacCamy, Victor J. Mizel
出版情報: London,[New York] : Macmillan, c1969  xiii, 561 p ; 24 cm
シリーズ名: Textbooks in applied mathematics
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5.

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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目次情報: 続きを見る
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
Stanley I. Grossman
出版情報: Orlando ; Tokyo : Academic Press, c1986  xiv, 876, 92, 10 p. ; 26 cm
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