Definitions and Terminology
Initial-Value Problems
Differential Equations as Mathematical Models

Solution Curves Without a Solution
Separable Variables
Linear Equations
Exact Equations
Solutions by Substitutions
A Numerical Method

Linear Models
Nonlinear Models
Modeling with Systems of First-Order DEs

Preliminary Theory—Linear Equations
Reduction of Order
Homogeneous Linear Equations with Constant Coefficients
Undetermined Coefficients—Superposition Approach
Undetermined Coefficients—Annihilator Approach
Variation of Parameters
Cauchy-Euler Equation
Solving Systems of Linear DEs by Elimination
Nonlinear Differential Equations

Linear Models: Initial-Value Problems 182
Linear Models: Boundary-Value Problems 199
Nonlinear Models 207