Topics Since Test2 (ODE stands for Ordinary Differential Equations, IVP
stands for an Initial Value Problem, i.e, the ODE plus initial conditions)
 1. Geometric series (part of 9.4: we regularly deposit any money or
	regularly take our medicine.)
 2. Knowing the order of a ODE and its relation to the number of arbitrary
	constants
 3. Using the initial conditions to find the value of the arbitrary constant(s)
	in the general solution. 
 4. Checking to see if a given function is a solution to a given ODE.
 5. Constructing slope fields from ODE.
 6. Constructing graphical solutions from the slope field.
 7. What existence and uniqueness of solutions of IVP says about the graphical
	solutions.
 8. Constructing numerical solutions.
	8A. Euler's method -- by hand.
	8B. Euler's method -- by calculator.
 9. Solving 1st order ODE's and IVP's using separation of variables.
10. Growth and decay examples: continuous compounded interest, exponential
	population growth, radioactive decay. the great lakes pollution removal.
11. Newton's law of cooling with examples.
12. Equilibrium solutions. Stable vs Unstable.
13. Modeling. (Perhaps the hardest section) Turning a physical problem
	into a ODE.
	13A. rate = rate in - rate out
	13B. rate is propotional to some function of the variable
	13C. concentration = quantity/volume
14. 2nd ODE I: Oscilations y''= - \omega^2 y.
	14A. Mass-spring system and Pendulum.
	14B. BVP, where the data is given at two points, instead of initial
		position and velocity as in a IVP.
15. 2nd ODE II: general linear constant coefficient case.
	15A. The characteristic poly of ay'' +by' +cy = 0 is ax^2+bx+c=0.
	15B. The relationship between the roots and the general solution.
	15C. Mass-spring with DAMPING.
	15D. Under/Over/Critical Damping.

Items in the text not covered:
We did not cover 10.7. But actually some of it got sneaked in, but we
didn't have problems in 10.7. In particular we can solve P' = k P and
P' = k P( a -P) which are the population equations in this section. We
just didn't do the modeling and didn't look at the real data.