目录 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
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