ELEMENTARY DIFFERENTIAL EQUATIONS [FREE PDF DOWNLOAD]

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TABLE OF CONTENT

Chapter 1 Introduction 1

1.1 Applications Leading to Differential Equations
1.2 First Order Equations 5
1.3 Direction Fields for First Order Equations 16

Chapter 2 First Order Equations 30

2.1 Linear First-Order Equations 30
2.2 Separable Equations 45
2.3 Existence and Uniqueness of Solutions of Nonlinear Equations 55
2.4 Transformation of Nonlinear Equations into Separable Equations 63
2.5 Exact Equations 73
2.6 Integrating Factors 83

Chapter 3 Numerical Methods

3.1 Euler’s Method 96
3.2 The Improved Euler Method and Related Methods 109
3.3 The Runge-Kutta Method 119

Chapter 4 Applications of First-Order Equations1em 130

4.1 Growth and Decay 130
4.2 Cooling and Mixing 140
4.3 Elementary Mechanics 151
4.4 Autonomous Second Order Equations 162
4.5 Applications to Curves 179

Chapter 5 Linear Second Order Equations

5.1 Homogeneous Linear Equations 194
5.2 Constant Coefficient Homogeneous Equations 210
5.3 Nonhomogeneous Linear Equations 221
5.4 The Method of Undetermined Coefficients I 229

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