Basic Introduction Title: Ordinary Differential Equations Author: Jiao Baocong, Wang Zaihong, Shi Hongyan ISBN: 9787302177616 Pages: 279 Pricing: 29.80 Yuan Press: Tsinghua University Press: 2008-08-0 1 Binding:. This book is divided into seven chapters: basic concepts, concise elementary content, focusing on revealing the essence of concepts, expounding the idea of theorems, introducing application methods and analysis examples, and introducing mathematical software that meets the content. Each chapter is equipped with exercises, all calculation questions have answers, and individual proof questions have tips. This book can be used as a teaching material for mathematics majors in normal colleges and universities of science and engineering and as a reference book for other science and engineering majors. Contents chapter 1 basic concepts 1. 1.1.2 basic concepts 1.2. 1 ordinary differential equations and partial differential equations1. .2 Chapter II Elementary Integration Method of First Order Equation 2. 1 Variable Separable Equation Exercise 2. 1 2.2 Homogeneous Equation Exercise 2.2.3 First Order Linear Equation Exercise 2.3 2.4 Fully Differential Equation 2.4. 1 Fully Differential Equation 2.4.2 Integral Factor Exercise 2.4 2.5 First Order Implicit Equation 2.5./klc 2 equation problem without explicit X 2.5 2.6 application example 2.6 initial value general theoretical mirror method 3. 1.3 Euler broken line problem 3. 1 3.2 piccard existence uniqueness theorem problem 3.2 3 continuity of solution exercise 3.3.4 continuity of solution to initial value exercise 3.4 3.5 differentiability of solution to initial value exercise 3.5 3.6 singular solution of first-order implicit equation 3.6. Discriminant curve method 3.6.3c? Discriminant curve method exercise 3.6 Chapter 4 Higher-order differential equation 4. 1 Higher-order differential equation 4. 1 Introduction to simplification method of higher-order differential equation 4. 1.2 Exercise 4. 1 4.2 Higher-order linear homogeneous differential equations 4.2.0 General theory of linear homogeneous differential equations 4.2.2 4.2.3 Solutions of some linear homogeneous differential equations with variable coefficients 4.2 4.3 Power series solutions of second-order linear homogeneous differential equations 4.3.4 Solutions in the neighborhood of regular singularities 4.3.4 Two special equation exercises 4.4.4 Higher-order linear nonhomogeneous differential equations 4.4.66. 4.4.2 General theory of solutions of linear nonhomogeneous differential equations with constant coefficients 4.4.5 Application examples 4.5. 1 spring vibration problem 4.5.2 Electromagnetic vibration problem 4.5.3 Solution of differential equations of spring vibration problem 4.5 Chapter 5 Differential equations 5. 1 Basic concepts of differential equations 5. .3 into higher-order equation method and integrable combination method Exercise 5. 1.5.2 General theory of linear homogeneous differential equation 5.2. 1 Solution Exercise 5.2 5.3 General theory of first-order linear inhomogeneous differential equation 5.3.655 Equation 5.3.2 Solution Exercise 5.3 5.4 Application Example 5.4/. Kloc-0/ steady state system 6. 1 dynamic system, Phase Space and Trajectory 6. 1.2 Trajectory Type Exercise 6. 1 6.2 Singularity of Plane Time-invariant System 6.2. 1 Singularity of Linear System 6.2.2 Singularity Exercise 6.2 6.3 Stability of Solution 6.3. 1 Concept of Lyapunov Stability 6.3.2 Judging Stability by Linear Approximation 6.3.3 Liapunov's Direct Method Exercise 6.3 6.4 Limit Cycle 6.4. 65438+ 1 First Order Nonlinear Difference Equation Exercise 7.2 7.3 General Theory of Higher Order Linear Difference Equation 7.3. 1 Simple Properties of Solutions 7.3.2 Structure of General Solutions 7.3.3 Abel Theorem Exercise 7.3 7.4 Solutions of Second Order Linear Difference Equations with Constant Coefficients 7.4.1rn ≡ 0 Case Exercise 7.4 Overview of the Development of Ordinary Differential Equations in Appendix A Answers and Tips in Appendix B