常微分方程及其應(yīng)用

內(nèi)容概要

　　《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)合多年的雙語教學(xué)經(jīng)驗編寫而成。全書共5章，包括一階線性微分方程，高階線性微分方程，線性微分方程組。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。書中配有大量的應(yīng)用實例和用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?！　”緯勺鳛楦叩仍盒＠砉た破砘蚍菙?shù)學(xué)專業(yè)的本科雙語教材，也可供相關(guān)專業(yè)的研究生、教師和廣大科技人員參考。

書籍目錄

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附錄　軟件包Iode簡介

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