Elementary Differential Equations

William Trench
A first course in ordinary differential equations.
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  • Chapter 1 Introduction 
    • 1.1 Applications Leading to Differential Equations
    • 1.2 First Order Equations 
    • 1.3 Direction Fields for First Order Equations 
  • Chapter 2 First Order Equations 
    • 2.1 Linear First Order Equations 
    • 2.2 Separable Equations 
    • 2.3 Existence and Uniqueness of Solutions of Nonlinear Equations 
    • 2.4 Transformation of Nonlinear Equations into Separable Equations 
    • 2.5 Exact Equations 
    • 2.6 Integrating Factors 
  • Chapter 3 Numerical Methods
    • 3.1 Euler’s Method 
    • 3.2 The Improved Euler Method and Related Methods 
    • 3.3 The Runge-Kutta Method 
  • Chapter 4 Applications of First Order Equations1em 
    • 4.1 Growth and Decay 
    • 4.2 Cooling and Mixing 
    • 4.3 Elementary Mechanics 
    • 4.4 Autonomous Second Order Equations 
    • 4.5 Applications to Curves 
  • Chapter 5 Linear Second Order Equations
    • 5.1 Homogeneous Linear Equations 
    • 5.2 Constant Coefficient Homogeneous Equations 
    • 5.3 Nonhomgeneous Linear Equations 
    • 5.4 The Method of Undetermined Coefficients I 
    • 5.5 The Method of Undetermined Coefficients II 
    • 5.6 Reduction of Order 
    • 5.7 Variation of Parameters 
  • Chapter 6 Applcations of Linear Second Order Equations 
    • 6.1 Spring Problems I 
    • 6.2 Spring Problems II 
    • 6.3 The RLC Circuit 
    • 6.4 Motion Under a Central Force 
  • Chapter 7 Series Solutions of Linear Second Order Equations
    • 7.1 Review of Power Series 
    • 7.2 Series Solutions Near an Ordinary Point I 
    • 7.3 Series Solutions Near an Ordinary Point II 
    • 7.4 Regular Singular Points Euler Equations 
    • 7.5 The Method of Frobenius I 
    • 7.6 The Method of Frobenius II 
    • 7.7 The Method of Frobenius III 
  • Chapter 8 Laplace Transforms
    • 8.1 Introduction to the Laplace Transform 
    • 8.2 The Inverse Laplace Transform 
    • 8.3 Solution of Initial Value Problems 
    • 8.4 The Unit Step Function 
    • 8.5 Constant Coefficient Equations with Piecewise Continuous Forcing Functions 
    • 8.6 Convolution 
    • 8.7 Constant Cofficient Equations with Impulses 
    • 8.8 A Brief Table of Laplace Transforms
  • Chapter 9 Linear Higher Order Equations
    • 9.1 Introduction to Linear Higher Order Equations 
    • 9.2 Higher Order Constant Coefficient Homogeneous Equations 
    • 9.3 Undetermined Coefficients for Higher Order Equations 
    • 9.4 Variation of Parameters for Higher Order Equations 
  • Chapter 10 Linear Systems of Differential Equations
    • 10.1 Introduction to Systems of Differential Equations 
    • 10.2 Linear Systems of Differential Equations 
    • 10.3 Basic Theory of Homogeneous Linear Systems 
    • 10.4 Constant Coefficient Homogeneous Systems I 
    • 10.5 Constant Coefficient Homogeneous Systems II 
    • 10.6 Constant Coefficient Homogeneous Systems II 
    • 10.7 Variation of Parameters for Nonhomogeneous Linear Systems
  • Student Solutions Manual. Worked out solutions for selected exercises
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