This textbook systematically introduces the elementary solution and basic theory of ordinary differential equations. The book mainly presents some methods that are used to solve the first order differential equations, higher order linear differential equations and systems of first order linear differential equations. Each chapter of this book is equipped with exercises for easy teaching and self-study.
This book can be used as a textbook or reference book for the course of ordinary differential equations for undergraduate students of various majors in mathematics departments of colleges and universities, and can be used as a reference for teachers and scientific researchers.
Chapter 2 First Order Differential Equations
2.1 Separable Equations
2.2 First Order Linear Equations
2.3 Exact Equations and Integrating Factors
2.4 Implicit First Order Differential Equations
2.5 Applications of First Order Equations
Chapter 3 Fundamental Theory of the First Order Differential Equations
3.1 The Existence and Uniqueness Theorem
3.2 Extension of Solutions
3.3 Continuous Dependence and Differentiability of Solutions with Respect to Initial Values
Chapter 4 Higher Order Linear Differential Equations
4.1 General Theory of nth Order Linear Differential Equations
4.2 Linear Differential Equations with Constant Coefficients
4.3 Reduction of Order
4.4 The Laplace Transform
Chapter 5 Systems of First Order Linear Differential Equations
5.1 The Concepts of Systems of Ordinary Differential Equations
5.2 Basic Theory of Systems of Linear Equations
5.3 Linear Systems with Constant Coefficients
Chapter 6 Nonlinear Differential Equations and Stability
6.1 Stability
6.2 The Method of Lyapunov
6.3 Stability Analysis of Two Biological Models
