# Elementary Differential Equations

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
Supplements:
• Student Solutions Manual. Worked out solutions for selected exercises
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