Ordinary Differential Equations with Applications, 2/e (Hardcover)

<內容簡介>

During the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE).

This useful book, which is based on the lecture notes of a well-received graduate course, emphasizes both theory and applications, taking numerous examples from physics and biology to illustrate the application of ODE theory and techniques.

Written in a straightforward and easily accessible style, this volume presents dynamical systems in the spirit of nonlinear analysis to readers at a graduate level and serves both as a textbook and as a valuable resource for researchers.

This new edition contains corrections and suggestions from the various readers and users. A new chapter on Monotone Dynamical Systems is added to take into account the new developments in ordinary differential equations and dynamical systems.
 
<章節目錄>

。Introduction

。Fundamental Theory

。Linear Systems

。Stability of Nonlinear Systems

。Method of Lyapunov Functions

。Two-Dimensional Systems

。Second Order Linear Equations

。The Index Theory and Brouwer Degree

。Perturbation Methods

。Introduction to Monotone Dynamical Systems

內容簡介：

在過去的三十年中，非線性分析、動態系統及其在科學和工程中的應用，激發了對常微分方程（ODE）理論的新興熱情。

這本實用的書籍基於一門受到好評的研究生課程的講義，強調理論和應用，並以物理學和生物學的眾多例子來說明ODE理論和技巧的應用。

本書以直觀易懂的風格撰寫，適合研究生級別的讀者，既可作為教材，也可作為研究人員的寶貴資源。

這個新版本包含了來自各個讀者和使用者的修正和建議。新增了一章關於單調動態系統的內容，以考慮常微分方程和動態系統的新發展。

章節目錄：

- 引言
- 基本理論
- 線性系統
- 非線性系統的穩定性
- Lyapunov函數方法
- 二維系統
- 二階線性方程
- 指數理論和Brouwer度
- 扰動方法
- 單調動態系統介紹