Ordinary Differential Equations with Applications, 2/e (Hardcover)
暫譯: 應用普通微分方程(第二版)(精裝本)

Sze-Bi Hsu

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商品描述

<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

商品描述(中文翻譯)

內容簡介

在過去三十年中,非線性分析、動力系統及其在科學和工程中的應用,重新激發了對常微分方程(Ordinary Differential Equations, ODE)理論的熱情。

這本有用的書籍基於一門廣受好評的研究生課程的講義,強調理論與應用,並從物理學和生物學中取出許多例子來說明ODE理論和技術的應用。

本書以簡單易懂的風格撰寫,向研究生讀者介紹動力系統,並同時作為教科書和研究人員的寶貴資源。

這一新版包含了來自各種讀者和使用者的修正和建議。新增了一章關於單調動力系統(Monotone Dynamical Systems),以考慮常微分方程和動力系統的新發展。

章節目錄

。引言

。基本理論

。線性系統

。非線性系統的穩定性

。李雅普諾夫函數法

。二維系統

。二階線性方程

。指數理論與布勞威爾度

。擾動方法

。單調動力系統簡介