《常微分方程及其應(yīng)用：理論與模型》是常微分方程課程的英文教材，是作者結(jié)合多年的雙語(yǔ)教學(xué)經(jīng)驗(yàn)編寫(xiě)而成。全書(shū)共5章，包括一階線(xiàn)性微分方程，高階線(xiàn)性微分方程，線(xiàn)性微分方程組。Laplace變換及其在微分方程求解中的應(yīng)用，以及微分方程的穩(wěn)定性理論。書(shū)中配有大量的應(yīng)用實(shí)例和用Matlab軟件繪制的微分方程解的相圖，并介紹了繪制相圖的程序。
本書(shū)可作為高等院校理工科偏理或非數(shù)學(xué)專(zhuān)業(yè)的本科雙語(yǔ)教材，也可供相關(guān)專(zhuān)業(yè)的研究生、教師和廣大科技人員參考。
Chapter 1 First．order Differential Equations
1．1 Introduction
Exercise 1．1
1．2 First—order Linear Differential Equations
1．2．1 First—order Homogeneous Linear Differential Equations
1．2．2 First—order Nonhomogeneous Linear Differential Equations
1．2．3 Bernoulli Equations
Exercise 1．2
1．3 Separable Equations
1．3．1 Separable Equations
1．3．2 Homogeneous Equations
Exercise 1．3
1．4 Applications
Module 1 The Spread of Technological Innovations
Module 2 The Van Meegeren Art Forgeries
1．5 Exact Equations
1．5．1 Criterion for Exactness
1．5．2 Integrating Factor
Exercise 1 5
1．6 Existence and Uniqueness of Solutions
Exercise 1．6
Chapter 2 Second．order Differential Equations
2．1 General Solutions of Homogeneous Second—order Linear Equations
Exercise 2．1
2．2 Homogeneous Second—order Linear Equations with Constant Coeffcients
2．2．1 The Characteristic Equation Has Distinct Real Roots
2．2．2 The Characteristic Equation Has Repeated Roots
2．2．3 The Characteristic Equation Has ComNeX Conjugate Roo~s
Exercise 2．2
2．3 Nonhomogeneous Second—order Linear Equations
2．3．1 Structure of General Solutions
2．3．2 Method of Variation of Parameters
2．3．3 Methods for Some Special Form of the Nonhomogeneous Term g(t)
Exercise 2．3
2．4 Applications
Module 1 An Atomic Waste Disposal Problem．
Module 2 Mechanical Vibrations
Chapter 3 Linear Systems of Differential Equations
3．1 Basic Concepts and Theorems
Exercise 3．1
3．2 The Eigenvalue-Eigenvector Method of Finding Solutions
3．2．1 The Characteristic Polynomial of A Has n Distinct Real
Eigenvalues
3．2．2 The Characteristic Polynomial of A Has Complex Eigenvalues
3．2．3 The Characteristic Polynomial of A Has Equal Eigenvalues
Exercise 3．2
3．3 YhndamentM Matrix Solution；Matrix—valued Exponential Function eAt
Exercise 3．3
3．4 Nonhomogeneous Equations；Variation of Parameters
Exercise 3．4
3．5 Applications
Module 1 The Principle of Competitive Exclusion in Population Biology．
Module 2 A Model for the Blood Glucose Regular System
Chapter 4 Laplace Transforms and Their Applications in Solving Differential Equations
4．1 Laplace Transforms
Exercise 4．1
4．2 Properties of Laplace Transforms
Exercise 4．2
4．3 Inverse Laplace Transforms
Exercise 4．3
4．4 Solving Differential Equations by Laplace Transforms
……
Chapter 5 Introduction to the Stability Theory
Answers to Selected Exercises
References
附錄 軟件包Iode簡(jiǎn)介
新書(shū)資訊