常微分方程及其应用

出版时间：2011-1  出版社：科学出版社  作者：周宇虹，罗建书 著  页数：224  

内容概要

　　《常微分方程及其应用：理论与模型》是常微分方程课程的英文教材，是作者结合多年的双语教学经验编写而成。全书共5章，包括一阶线性微分方程，高阶线性微分方程，线性微分方程组。Laplace变换及其在微分方程求解中的应用，以及微分方程的稳定性理论。书中配有大量的应用实例和用Matlab软件绘制的微分方程解的相图，并介绍了绘制相图的程序。　　本书可作为高等院校理工科偏理或非数学专业的本科双语教材，也可供相关专业的研究生、教师和广大科技人员参考。

书籍目录

Chapter 1　First．order Differential Equations1．1　　IntroductionExercise 1．11．2　First—order Linear Differential Equations1．2．1 First—order Homogeneous Linear Differential Equations1．2．2 First—order Nonhomogeneous Linear Differential Equations1．2．3 Bernoulli EquationsExercise 1．21．3　Separable Equations1．3．1　Separable Equations1．3．2 Homogeneous EquationsExercise 1．31．4 ApplicationsModule 1 The Spread of Technological InnovationsModule 2　The Van Meegeren Art Forgeries1．5　Exact Equations1．5．1　Criterion for Exactness1．5．2 Integrating FactorExercise 1 51．6　Existence and Uniqueness of SolutionsExercise 1．6Chapter 2　Second．order Differential Equations2．1　General Solutions of Homogeneous Second—order Linear EquationsExercise 2．12．2　Homogeneous Second—order Linear Equations with Constant Coeffcients2．2．1 The Characteristic Equation Has Distinct Real Roots2．2．2 The Characteristic Equation Has Repeated Roots2．2．3　The Characteristic Equation Has ComNeX Conjugate Roo~sExercise 2．22．3 Nonhomogeneous Second—order Linear Equations2．3．1　Structure of General Solutions2．3．2　Method of Variation of Parameters2．3．3　Methods for Some Special Form of the Nonhomogeneous Term g(t)Exercise 2．32．4　ApplicationsModule 1 An Atomic Waste Disposal Problem．Module 2　Mechanical VibrationsChapter 3　Linear Systems of Differential Equations3．1　Basic Concepts and TheoremsExercise 3．13．2　The Eigenvalue-Eigenvector Method of Finding Solutions3．2．1　The Characteristic Polynomial of A Has n Distinct RealEigenvalues3．2．2 The Characteristic Polynomial of A Has Complex Eigenvalues3．2．3 The Characteristic Polynomial of A Has Equal EigenvaluesExercise 3．23．3　YhndamentM Matrix Solution；Matrix—valued Exponential Function eAtExercise 3．33．4 Nonhomogeneous Equations；Variation of ParametersExercise 3．43．5 ApplicationsModule 1　The Principle of Competitive Exclusion in Population Biology．Module 2　A Model for the Blood Glucose Regular SystemChapter 4　Laplace Transforms and Their Applications in Solving Differential Equations4．1　Laplace TransformsExercise 4．14．2　Properties of Laplace TransformsExercise 4．24．3　Inverse Laplace TransformsExercise 4．34．4　Solving Differential Equations by Laplace Transforms……Chapter 5 Introduction to the Stability TheoryAnswers to Selected ExercisesReferences附录　软件包Iode简介