Background
Solutions and Initial Value Problems
Direction Fields
The Approximation Method of Euler
1. Introduction
Background
Solutions and Initial Value Problems
Direction Fields
The Approximation Method of Euler
2. First Order Differential Equations
Introduction: Motion of a Falling Body
Separable Equations
Linear Equations
Exact Equations
Special Integrating Factors
Substitutions and Transformations
4. Linear Second Order Equations
Introduction: The Simple Pendulum
Linear Differential Operators
Fundamental Solutions of Homogeneous Equations
Reduction of Order
Homogeneous Linear Equations with Constant Coefficients
Auxiliary Equations with Complex Roots
Superposition and Nonhomogeneous Equations
Method of Undetermined Coefficients
Variation of Parameters
5. Applications and Numerical Methods for Second Order Equations and Systems
Mechanical Vibrations and Simple Harmonic Motion
Damped Free Vibrations
Forced Vibrations
Electric Circuits
7. Laplace Transforms
Definition of the Laplace Transform
Properties of the Laplace Transform
Inverse Laplace Transform
Solving Initial Value Problems
Transforms of Discontinuities and Periodic Functions
Convolution
Impluses and the Dirac Delta Function
8. Series solution of Differential
Equations
Power Series, Analytic Functions, and the Taylor Series Method