Monday, September 3; Labor Day
Sometimes, rather than explicitly solving a differential equation, it is useful to try to visualize the solutions. To this end, we discuss slope fields and how to plot solution curves. We also discuss two theorems about the existence and uniqueness of solutions (one of which is not in the book). For Wednesday, read Section 1.4. Homework 1, over Sections 1.1-1.2 is due Wednesday at the beginning of class.
Wednesday, September 5
Separable equations. This is our first chance to solve differential equations in a way that is not a simple calculus application. These equations will have x and y on the right hand side, but in a way that they can be pulled apart multiplicatively. At the beginning of class, we experiment a little with an applet that draws slope fields and solution curves for us. For Friday, read Section 1.5.
Friday, September 7
A new type of solvable equations is dealt with today: firs order linear equations. These have the form y'+P(x)y=Q(x), for some functions P and Q. We find a special term, called an integrating factor, that turns reduces the process of solving the d.e. to finding two integrals. For next time, read Section 1.6