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Unformatted text preview: C O N T E N T S Preface vii Chapter 1 Introduction 1 1.1 Some Basic Mathematical Models; Direction Fields 1 1.2 Solutions of Some Differential Equations 9 1.3 Classification of Differential Equations 17 1.4 Historical Remarks 23 Chapter 2 First Order Differential Equations 29 2.1 Linear Equations with Variable Coefficients 29 2.2 Separable Equations 40 2.3 Modeling with First Order Equations 47 2.4 Differences Between Linear and Nonlinear Equations 64 2.5 Autonomous Equations and Population Dynamics 74 2.6 Exact Equations and Integrating Factors 89 2.7 Numerical Approximations: Euler’s Method 96 2.8 The Existence and Uniqueness Theorem 105 2.9 First Order Difference Equations 115 Chapter 3 Second Order Linear Equations 129 3. 1 Homogeneous Equations with Constant Coefficients 129 3. 2 Fundamental Solutions of Linear Homogeneous Equations 137 3. 3 Linear Independence and the Wronskian 147 3. 4 Complex Roots of the Characteristic Equation 153 3. 5 Repeated Roots; Reduction of Order 160 3. 6 Nonhomogeneous Equations; Method of Undetermined Coefficients...
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