微分方程定性理論

作　者：張芷芬著 叢 書 名：現代數學基礎叢書

版　次：1

頁　數：550

裝　幀：平裝

開　本：32開

所屬分類：圖書 > 科學與自然 > 數學

《微分方程定性理論》是作者在常微分方程定性理論的多年教學和科研工作的基礎上寫成的，著重介紹平面定性理論的主要內容和方法，重點是：平面奇點，極限環的存在，唯一性及個數，無窮遠奇點，二維周期系統的調和解，環面上的常微系統，二維流形上的結構穩定性。《微分方程定性理論》各章均附有習題。

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. Limit 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