微分方程的定性理論（全英文） 下載 mobi epub pdf 電子書 2024

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內容簡介

書中主要講解瞭微分方程理論的基本方法，對微分方程的存在性、連續依賴性、穩定性、周期解、自治微分係統、動力係統等基本問題進行詳細分析，並注重理論間的聯係。《微分方程的定性理論》基礎性強、應用廣泛，是一本適閤大學高年級選修課、研究生雙語教學以及讀者自學的英文教科書。

作者簡介

劉和濤，教授，留美執教數十年，曾在培生教育等國際著名、齣版機構齣版過多種教材，為美國多所院校采用。本教材秉承瞭國外先進教學理念，並針對國內學生實際情況，尤其注、意瞭由淺入深的理論過渡，建立瞭完備的邏輯體係，語言地、道，是適閤於雙語教學的優秀教科書，亦適閤學生自學。

目錄

Preface

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. Liapunovs 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

精彩書摘

The study of linear differential equations is very important for the fol-lowing reasons. First， the study provides us with some basic knowledgefor understanding general nonlinear differential equations. Second， manynonlinear differential equations can be written as summations of linear dif-ferential equations and some small nonlinear perturbations. Thus， undercertain conditions， the qualitative properties of linear differential equationscan be used to infer essentially the same qualitative properties for nonlineardifferential equations.

前言/序言

　　Differential equations are mainly used to describe the changes of quanti-ties or behavior of certain systems in applications， such as those governedby Newtons laws in physics.
　　When the differential equations under study are linear， the conventionalmethods， such as the Laplace transform method and the power series solu-tions， can be used to solve the differential equations analytically， that is， thesolutions can be written out using formulas.
　　When the differential equations under study are nonlinear， analytical so-lutions cannot， in general， be found; that is， solutions cannot be writtenout using formulas. In those cases， one approach is to use numerical ap-proximations. In fact， the recent advances in computer technology makethe numerical approximation classes very popular because powerful softwareallows students to quickly approximate solutions of nonlinear differentialequations and visualize their properties.
　　However， in most applications in biology， chemistry， and physics mod-eled by nonlinear differential equations where analytical solutions may beunavailable， people are interested in the questions related to the so-calledqualitative properties， such as： will the system have at least one solu-tion？ will the system have at most one solution？ can certain behavior ofthe system be controlled or stabilized？ or will the system exhibit some peri-odicity？ If these questions can be answered without solving the differentialequations， especially when analytical solutions are unavailable， we can stillget a very good understanding of the system. Therefore， besides learningsome numerical methods， it is also important and beneficial to learn howto analyze some qualitative properties.

微分方程的定性理論（全英文） 下載 mobi epub pdf txt 電子書 格式

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