微分方程定性理论

《微分方程定性理论》是1997年1月1日科学出版社出版的图书，作者是张芷芬。本书主要描述了平面定性理论的主要内容和方法。

基本相信

作　者：张芷芬著 丛 书 名：现代数学基础丛书

版　次：1

页　数：550

装　帧：平装

开　本：32开

所属分类：图书 \u003e 科学与自然 \u003e 数学

内容简介

《微分方程定性理论》是作者在常微分方程定性理论的多年教学和科研工作的基础上写成的，着重介绍平面定性理论的主要内容和方法，重点是：平面奇点，极限环的存在，唯一性及个数，无穷远奇点，二维周期系统的调和解，环面上的常微系统，二维流形上的结构稳定性。《微分方程定性理论》各章均附有习题。

目录

reface

Chapter 1 A Brief Description

1. Linear Differential Equations

2. The Need for Qualitative Analysis

3. Description and Terminology

Chapter 2 Existence and Uniqueness

1. Introduction

2. Existence and Uniqueness

3. Dependence on Initial Data and Parameters

4. Maximal Interval of Existence

5. Fixed Point Method

Chapter 3 Linear Differential Equations

1. Introduction

2. General Nonhomogeneous Linear Equations

3. Linear Equations with Constant Coefficients

4. Periodic Coefficients and Floquet Theory

Chapter 4 Autonomous Differential Equations in R2

1. Introduction

2. Linear Autonomous Equations in R2

3. Perturbations on Linear Equations in R2

4. An Application: A Simple Pendulum

Chapter 5 Stability

1. Introduction

2. Linear Differential Equations

3. Perturbations on Linear Equations

4. Liapunov's Method for Autonomous Equations

Chapter 6 Periodic Solutions

1. Introduction

2. Linear Differential Equations

3. Nonlinear Differential Equations

Chapter 7 Dynamical Systems

1. Introduction

2. Poincare-Bendixson Theorem in R2

3. 极限 Cycles

4. An Application: Lotka-Volterra Equation

Chapter 8 Some New Equations

1. Introduction

2. Finite Delay Differential Equations

3. INFINITE Delay Differential Equations

4. Integrodifferential Equations

5. Impulsive Differential Equations

6. Equations with Nonlocal Conditions

7. Impulsive Equations with Nonlocal Conditions

8. Abstract Differential Equations

Appendix

References

Index

参考资料

Warning: Invalid argument supplied for foreach() in /www/wwwroot/newbaike.com/id.php on line 280