# Lecture Outlines

### August | September | October | November | December

**Monday, August 27**

Today is the first day of class. We begin by discussing
what a differential equation is and what possible applications might be. Where might you
have seen them before? Where can yo imagine them emerging. Also, a discussion of the syllabus
and the structure of the course, and an illustrative example: the Lotka-Volterra predator-prey
system. Read Section 1.1 for Wednesday.

**Wednesday, August 29**

Today, we discuss ways of classifying differential equations.
Autonomous v. Non-autonomous, Linear v. Non-linear, Ordinary v. Partial. Also, we talk about what we
mean when we ask for a "solution" to a differential equation. Read Section 1.2 for Friday.

**Friday, August 31**

Our first method for finding solutions of differential equation is
presented in this class. For equations of the form y'=ƒ(x), which depend only on x on the right hand
side, we can find a solution by just integrating. This knowledge lets us re-create the laws of motion
under constant acceleration from physics. For Monday, read Section 1.3.