Chapter 1 First.order Differential Equations
1.1 Introduction
Exercise 1.1
1.2 First—order Linear Differential Equations
1.2.1 First—order Homogeneous Linear Differential Equations
1.2.2 First—order Nonhomogeneous Linear Differential Equations
1.2.3 Bernoulli Equations
Exercise 1.2
1.3 Separable Equations
1.3.1 Separable Equations
1.3.2 Homogeneous Equations
Exercise 1.3
1.4 Applications
Module 1 The Spread of Technological Innovations
Module 2 The Van Meegeren Art Forgeries
1.5 Exact Equations
1.5.1 Criterion for Exactness
1.5.2 Integrating Factor
Exercise 1 5
1.6 Existence and Uniqueness of Solutions
Exercise 1.6
Chapter 2 Second.order Differential Equations
2.1 General Solutions of Homogeneous Second—order Linear Equations
Exercise 2.1
2.2 Homogeneous Second—order Linear Equations with Constant Coeffcients
2.2.1 The Characteristic Equation Has Distinct Real Roots
2.2.2 The Characteristic Equation Has Repeated Roots
2.2.3 The Characteristic Equation Has ComNeX Conjugate Roo~s
Exercise 2.2
2.3 Nonhomogeneous Second—order Linear Equations
2.3.1 Structure of General Solutions
2.3.2 Method of Variation of Parameters
2.3.3 Methods for Some Special Form of the Nonhomogeneous Term g(t)
Exercise 2.3
2.4 Applications
Module 1 An Atomic Waste Disposal Problem.
Module 2 Mechanical Vibrations
Chapter 3 Linear Systems of Differential Equations
3.1 Basic Concepts and Theorems
Exercise 3.1
3.2 The Eigenvalue-Eigenvector Method of Finding Solutions
3.2.1 The Characteristic Polynomial of A Has n Distinct Real
Eigenvalues
3.2.2 The Characteristic Polynomial of A Has Complex Eigenvalues
3.2.3 The Characteristic Polynomial of A Has Equal Eigenvalues
Exercise 3.2
3.3 YhndamentM Matrix Solution;Matrix—valued Exponential Function eAt
Exercise 3.3
3.4 Nonhomogeneous Equations;Variation of Parameters
Exercise 3.4
3.5 Applications
Module 1 The Principle of Competitive Exclusion in Population Biology.
Module 2 A Model for the Blood Glucose Regular System
Chapter 4 Laplace Transforms and Their Applications in Solving Differential Equations
4.1 Laplace Transforms
Exercise 4.1
4.2 Properties of Laplace Transforms
Exercise 4.2
4.3 Inverse Laplace Transforms
Exercise 4.3
4.4 Solving Differential Equations by Laplace Transforms
……
Chapter 5 Introduction to the Stability Theory
Answers to Selected Exercises
References
附录 软件包Iode简介