Exam I will cover the following sections of the textbook: 1.1-1.3, 2.1 - 2.6, and 3.1. In preparing for the exam, it's a good idea to look over your homework / try additional problems / work through examples in the text.

Some additional practice problems can be found here.

A list of topics is given below:

• Classification of different types of differential equations: you should be able to determine the order of a differential equation, whether it is linear or nonlinear, and know the solution methods corresponding to these different types of equations.
• Graphical methods for solving differential equations
  • Slope fields
  • Plotting dy/dt vs. y for autonomous first order equations
  • Equilibria / stability / long term behavior
• Linear first order ODEs
  • Separable equations
  • Integrating factors
  • Exact equations
• Constructing and solving mathematical models using differential equations
• Existence and uniqueness of solutions
  • Linear first order equations
  • Nonlinear first order equations
• Second order linear homogeneous differential equations
  • Exponential solutions and the characteristic equaiton
  • Superposition of solutions