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 Complex Conjugate Roots 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 Fundamental 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 4.4.1 The Right-Hand Side of the Differential Equation is Discontinuous 4.4.2 The Right-Hand Side of Differential Equation is an Impulsive Function Exercise 4.4 4.5 Solving Systems of Differential Equations by Laplace Transforms Exercise 4.5 Chapter 5 Introduction to the Stability Theory 5.1 Introduction Exercise 5.1 5.2 Stability of the Solutions of Linear System Exercise 5.2 5.3 Geometrical Characteristics of Solutions of the System of Differential Equations 5.3.1 Phase Space and Direction Field 5.3.2 Geometric Characteristics of the Orbits near a Singular Point 5.3.3 Stability of Singular Points Exercise 5.3 5.4 Applications Module 1 Volterra\\\'s Principle Module 2 Mathematical Theories of War Answers to Selected Exercises References 附录 软件包Iode简介
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