# Math 53 Midterm Review

On the midterm, you can use your book and notes. You cannot use calculators, computers, or the assistance of other people.

Many of the questions will be computational, e.g. solve a differential equation. For these questions, you should be able to check if your answers are correct. There will also be a few conceptual short-answer questions, e.g. true/false questions. There will be no proofs.

The following topics may be covered:

• Solving and understanding simple first-order equations.
• Separable equations.
• Linear equations.
• Exact equations and substitution methods.
• Autonomous equations (equilibrium, stability, etc.).
• Linear equations of higher order.
• General theory.
• Vector spaces of functions, and linear operators.
• Homogeneous/inhomogeneous equations, complementary/particular solutions.
• Solving constant coefficient linear homogeneous equations.
• Finding particular solutions to inhomogeneous linear equations.
• Very simple systems of differential equations. (You won't need eigenvalues.)