常微分方程（英文版）

图书信息

作者：刘超，姜玉山，东北大学 | 分类：科学技术,自然科学,数学

作者简介

作者简介 暂缺《常微分方程（英文版）》作者简介

内容简介

内容简介 　　本教材共分为5章，具体介绍一阶常微分方程初等解法，齐次线性微分方程一般解法、非齐次线性微分方程的常数变易法、非齐次线性微分方程伯努利方程解法，一阶常微分方程积分因子求法以及四类隐式微分方程的解法，一阶微分方程的解的存在性定理以及延拓性定理，高阶微分方程的常数变易法以及非齐次（齐次）常系数高阶微分方程的解法（待定系数法），变系数高阶微分方程的解法，矩阵指数求法，一阶线性微分方程组解的结构以及解的存在性定理，非线性微分系统的稳定性理论等知识点。

目录

图书目录
Chapter 1 Elementary Integration Methods1.1 Differential equations and solutions1.2 Variable separable equation1.3 Homogeneous differential equations1.4 First-order linear differential equations1.5 Total differential equations and integration factors1.6 First-order implicit differential equation1.7 Several high-orderequationsChapter 2 Fundamental Theorems.2.1 Existence and uniqueness theorem2.2 Theorem of existence and uniqueness of solution2.3 Extension of the solution2.4 Strange solution2.5 Continuous dependence on initial value of the solutionChapter 3 Linear Differential Equations3.1 First order differential equations3.2 General concepts of first-order linear differential equations3.3 General theory of first-order linear homogeneous systems3.4 General theory of first-order linear non-homogeneous systems3.5 Solution of linear differential equations with constant coefficients3.6 The solution method for linear differential equations(complex and multiple root)Chapter 4 Linear Differential Equations4.1 General theory of n-order linear differential equations4.2 Solution of n-th order constant coefficient linear homogeneous equation4.3 N-th order constant coefficient linear non-homogeneous equation solution4.4 Second-order constant coefficient linear equations and vibration phenomenaChapter 5 Introduction to Qualitative and Stability Theory5.1 Concept of stability5.2 Lyapunov's second method5.3 Basic concepts of plane autonomous system5.4 Introduction to plane qualitative theory