Preface
CHAPTER ONE INTRODUCTION TO DIFFERENTIAL EQUATIONS
1-1 Differential Equations in Sciences and Engineering
1-2 How do Differential Equations Arise?
1-3 A Brief Review of Basic Concepts
Dependent and Independent Variables
Continuous and Discontinuous Functions
Derivatives and Differentials
Integration
1-4 Classification of Differential Equations
1-5 Solutions of Differential Equations
1-6 Solving Differential Equations by Direct Integration
1-7 Introduction to Computer Methods
Plotting Solutions
Symbolic Integration
The Special Functions of Mathematics
Numerical Integration
Considerations for Computer Solution of a Differential Equation
1-8 Summary
Problems
CHAPTER TWO FIRST-ORDER DIFFERENTIAL EQUATIONS
2-1 An Overview of First-Order Differential Equations
2-2 Linear First-Order Equations
Integrating Factor
A Special Case: Equations with Constant Coefficients and Constant Right-Hand Side
Existence and Uniqueness of Solutions
Section Review
2-3 Applications of First-Order Linear Equations
Estimating the Response Time with the Time Constant
Section Review
2-4 Nonlinear First-Order Differential Equations
Section Review
2-5 Separable First-Order Equations
Orthogonal Trajectories and Differential Equations
Transforming Nonseparable Equations into Separable Ones
Homogeneous Differential Equations
Section Review
2-6 Exact First-Order Differential Equations
Definition of An Exact Differential Equation
Alternative Solution: Method of Grouping
Integrating Factors
Section Review
2-7 Graphical Methods
Section Review
2-8 A Systematic Approach to Solving
First-Order Equations
2-9 Computer Methods for First-Order Equations
Obtaining Closed-Form Solutions
Generating Contour Plots
Obtaining Direction Field Plots
2-10 Summary
Problems
CHAPTER THREE SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS
3-1 Introduction to Second-Order Linear Equations
Section Review
CHAPTER FOUR HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONS
CHAPTER FIVE LINEAR DIFFERENTIAL EQUMIONS: VARIABLE COEFFICENTS
CHAPTER SIX SYSTEMS OF LINEAR DIFFERENTIAL EQUMIONS: SCALAR APPROACH
CHAPTER SEVEN SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS: MATRIX APPROACH
CHAPTER EIGHT LAPLACE TRANSFORMS
CHAPTER NINE NUMERICAL SOLUTION OF DIFFERENTIAL EQUMIONS
编辑手记

本书主要包括科学和工程学中的微分方程基本概念，一级、二级和高级微分方程的分类、扩展和应用，线性微分方程，可变系数，线性微分方程体系的标量近似，线性微分方程体系的矩阵方法，拉普拉斯变换的基本性质，微分方程的数值解和数值方法的失误等内容。