微分方程、动力系统与混沌引论（第3版英文版）

作者: Morris 著 , W.Hirsch 著 , Stephen 著 , Smale 著 , Robert 著

出版社: 世界图书出版公司

出版时间: 2016-01

版次: 1

ISBN: 9787519200138

定价: 75.00

装帧: 平装

开本: 24开

纸张: 胶版纸

页数: 418页

字数: 788千字

正文语种: 英语

分类: 自然科学

　　《微分方程、动力系统与混沌引论（第3版英文版）》涵盖了常微分方程在动力系统方面的应用。《微分方程、动力系统与混沌引论（第3版英文版）》探究了动力系统与纯数学之外的特定场之间的关系，并且依然是该研究领域内研究生的标准教材。《微分方程、动力系统与混沌引论（第3版英文版）》市专门为有计算和初级线性代数基础的学生书写的，因此虽然有点枯燥，但是还在可接受的范围，而且包含了一些例子和探究去巩固学习。 Morris W. Hirsch(M.W.赫希，美国）是国际知名学者，在数学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。 Preface to the Third Edition
Preface
CHAPTER 1 First-Order Equations
1．1 The Simplest Example
1．2 The Logistic Population Model
1．3 Constant Harvesting and Bifurcations
1．4 Periodic Harvesting and Periodic Solutions
1．5 Computing the Poincare Map
1．6 Exploration： A Two-Parameter Family

CHAPTER 2 Planar Linear Systems
2．1 Second-Order Differential Equations
2．2 Planar Systems
2．3 Preliminaries from Algebra
2．4 Planar Linear Systems
2．5 Eigenvalues and Eigenvectors
2．6 Solving Linear Systems
2．7 The Linearity Pnnciple

CHAPTER 3 Phase Portraits for Planar Systems
3．1 Real Distinct Eigenvalues
3．2 Complex Eigenvalues
3．3 Repeated Eigenvalues
3．4 Changing Coordinates

CHAPTER 4 Classification of Planar Systems
4．1 The Trace-Determinant Plane
4．2 Dynamical Classification
4．3 Exploration： A 3D Parameter Space

CHAPTER 5 Higher-Dimensional Linear Algebra
5．1 Preliminaries from Linear Algebra
5．2 Eigenvalues and Eigenvectors
5．3 Complex Eigenvalues
5．4 Bases and Subspaces
5．5 Repeated Eigenvalues
5．6 Genericity

CHAPTER 6 Higher-Dimensional Linear Systems
6．1 Distinct Eigenvalues
6．2 Harmonic Oscillators
6．3 Repeated Eigenvalues
6．4 The Exponential of a Matrix
6．5 Nonautonomous Linear Systems

CHAPTER 7 Nonlinear Systems
7．1 Dynamical Systems
7．2 The Existence and Uniqueness Theorem
7．3 Continuous Dependence of Solutions
7．4 The Variational Equation
7．5 Exploration： Numerical Methods
7．6 Exploration： Numerical Methods and Chaos

CHAPTER 8 Equilibria in Nonlinear Systems
8．1 Some Illustrative Examples
8．2 Nonlinear Sinks and Sources
8．3 Saddles
8．4 Stability
8．5 Bifurcations
8．6 Exploration： Complex Vector Fields

CHAPTER 9 Global Nonlinear Techniques
9．1 Nullclines
9．2 Stability of Equilibria
9．3 Gradient Systems
9．4 Hamiltonian Systems
9．5 Exploration： The Pendulum with Constant Forcing

CHAPTER 10 Closed Orbits and Limit Sets
10．1 Limit Sets
10．2 Local Sections and Flow Boxes
10．3 The Poincare Map
10．4 Monotone Sequences in Planar Dynamical Systems
10．5 The Poincare-Bendixson Theorem
10．6 Applications of Poincare-Bendixson
10．7 Exploration： Chemical Reactions that Oscillate

CHAPTER 11 Applications in Biology
11．1 Infectious Diseases
11．2 Predator-Prey Systems
11．3 Competitive Species
11．4 Exploration： Competition and Harvesting
11．5 Exploration： Adding Zombies to the SIR Model

CHAPTER 12 Applications in Circuit Theory
12．1 An RLC Circuit
12．2 The Lienard Equation
12．3 The van der Pol Equation
12．4 A Hopf Bifurcation
12．5 Exploration： Neurodynamics

CHAPTER 13 Applications in Mechanics
13．1 Newton's Second Law
13．2 Conservative Systems
13．3 Central Force Fields
13．4 The Newtonian Central Force System
13．5 Kepler's First Law
13．6 The Two-Body Problem
13．7 Blowing Up the Singularity
13．8 Exploration： Other Centrai Force Problems
13．9 Exploration： Classical Limits of Quantum Mechanical Systems
13．10 Exploration： Motion of a Glider

CHAPTER 14 The Lorenz System
14．1 Introduction
14．2 Elementary Properties of the Lorenz System
14．3 The Lorenz Attractor
14．4 A Modef for the Lorenz Attractor
14．5 The Chaotic Attractor
14．6 Exploration： The Rossler Attractor

CHAPTER 15 Discrete Dynamical Systems
15．1 Introduction
15．2 Bifurcations
15．3 The Discrete Logistic Model
15．4 Chaos
15．5 Symbolic Dynamics
15．6 The Shift Map
15．7 The Cantor Middle-Thirds Set
15．8 Exploration：Cubic Chaos
15．9 Exploration： The Orbit Diagram

CHAPTER 16 Homoclinic Phenomena
16．1 The Shilnikov System
16．2 The Horseshoe MaD
16．3 The Double Scroll Attractor
16．4 Homoclinic Bifurcations
16．5 Exploration： The Chua Circuit

CHAPTER 17 Existence and Uniqueness Revisited
17．1 The Existence and Uniqueness Theorem
17．2 Proof of Existence and Uniqueness
17．3 Continuous Dependence on Initial Conditions
17．4 Extending Solutions
17．5 Nonautonomous Systems
17．6 Differentiability of the Flow
Bibliography
Index
内容简介:
　　《微分方程、动力系统与混沌引论（第3版英文版）》涵盖了常微分方程在动力系统方面的应用。《微分方程、动力系统与混沌引论（第3版英文版）》探究了动力系统与纯数学之外的特定场之间的关系，并且依然是该研究领域内研究生的标准教材。《微分方程、动力系统与混沌引论（第3版英文版）》市专门为有计算和初级线性代数基础的学生书写的，因此虽然有点枯燥，但是还在可接受的范围，而且包含了一些例子和探究去巩固学习。
作者简介:
Morris W. Hirsch(M.W.赫希，美国）是国际知名学者，在数学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
目录:
Preface to the Third Edition
Preface
CHAPTER 1 First-Order Equations
1．1 The Simplest Example
1．2 The Logistic Population Model
1．3 Constant Harvesting and Bifurcations
1．4 Periodic Harvesting and Periodic Solutions
1．5 Computing the Poincare Map
1．6 Exploration： A Two-Parameter Family

CHAPTER 2 Planar Linear Systems
2．1 Second-Order Differential Equations
2．2 Planar Systems
2．3 Preliminaries from Algebra
2．4 Planar Linear Systems
2．5 Eigenvalues and Eigenvectors
2．6 Solving Linear Systems
2．7 The Linearity Pnnciple

CHAPTER 3 Phase Portraits for Planar Systems
3．1 Real Distinct Eigenvalues
3．2 Complex Eigenvalues
3．3 Repeated Eigenvalues
3．4 Changing Coordinates

CHAPTER 4 Classification of Planar Systems
4．1 The Trace-Determinant Plane
4．2 Dynamical Classification
4．3 Exploration： A 3D Parameter Space

CHAPTER 5 Higher-Dimensional Linear Algebra
5．1 Preliminaries from Linear Algebra
5．2 Eigenvalues and Eigenvectors
5．3 Complex Eigenvalues
5．4 Bases and Subspaces
5．5 Repeated Eigenvalues
5．6 Genericity

CHAPTER 6 Higher-Dimensional Linear Systems
6．1 Distinct Eigenvalues
6．2 Harmonic Oscillators
6．3 Repeated Eigenvalues
6．4 The Exponential of a Matrix
6．5 Nonautonomous Linear Systems

CHAPTER 7 Nonlinear Systems
7．1 Dynamical Systems
7．2 The Existence and Uniqueness Theorem
7．3 Continuous Dependence of Solutions
7．4 The Variational Equation
7．5 Exploration： Numerical Methods
7．6 Exploration： Numerical Methods and Chaos

CHAPTER 8 Equilibria in Nonlinear Systems
8．1 Some Illustrative Examples
8．2 Nonlinear Sinks and Sources
8．3 Saddles
8．4 Stability
8．5 Bifurcations
8．6 Exploration： Complex Vector Fields

CHAPTER 9 Global Nonlinear Techniques
9．1 Nullclines
9．2 Stability of Equilibria
9．3 Gradient Systems
9．4 Hamiltonian Systems
9．5 Exploration： The Pendulum with Constant Forcing

CHAPTER 10 Closed Orbits and Limit Sets
10．1 Limit Sets
10．2 Local Sections and Flow Boxes
10．3 The Poincare Map
10．4 Monotone Sequences in Planar Dynamical Systems
10．5 The Poincare-Bendixson Theorem
10．6 Applications of Poincare-Bendixson
10．7 Exploration： Chemical Reactions that Oscillate

CHAPTER 11 Applications in Biology
11．1 Infectious Diseases
11．2 Predator-Prey Systems
11．3 Competitive Species
11．4 Exploration： Competition and Harvesting
11．5 Exploration： Adding Zombies to the SIR Model

CHAPTER 12 Applications in Circuit Theory
12．1 An RLC Circuit
12．2 The Lienard Equation
12．3 The van der Pol Equation
12．4 A Hopf Bifurcation
12．5 Exploration： Neurodynamics

CHAPTER 13 Applications in Mechanics
13．1 Newton's Second Law
13．2 Conservative Systems
13．3 Central Force Fields
13．4 The Newtonian Central Force System
13．5 Kepler's First Law
13．6 The Two-Body Problem
13．7 Blowing Up the Singularity
13．8 Exploration： Other Centrai Force Problems
13．9 Exploration： Classical Limits of Quantum Mechanical Systems
13．10 Exploration： Motion of a Glider

CHAPTER 14 The Lorenz System
14．1 Introduction
14．2 Elementary Properties of the Lorenz System
14．3 The Lorenz Attractor
14．4 A Modef for the Lorenz Attractor
14．5 The Chaotic Attractor
14．6 Exploration： The Rossler Attractor

CHAPTER 15 Discrete Dynamical Systems
15．1 Introduction
15．2 Bifurcations
15．3 The Discrete Logistic Model
15．4 Chaos
15．5 Symbolic Dynamics
15．6 The Shift Map
15．7 The Cantor Middle-Thirds Set
15．8 Exploration：Cubic Chaos
15．9 Exploration： The Orbit Diagram

CHAPTER 16 Homoclinic Phenomena
16．1 The Shilnikov System
16．2 The Horseshoe MaD
16．3 The Double Scroll Attractor
16．4 Homoclinic Bifurcations
16．5 Exploration： The Chua Circuit

CHAPTER 17 Existence and Uniqueness Revisited
17．1 The Existence and Uniqueness Theorem
17．2 Proof of Existence and Uniqueness
17．3 Continuous Dependence on Initial Conditions
17．4 Extending Solutions
17．5 Nonautonomous Systems
17．6 Differentiability of the Flow
Bibliography
Index