ABSTRACT
There are two parts to this chapter. The first is a discussion of the proofs of the main theorems in the previous chapter. This discussion contains a fairly complete and rigorous verification of the big theorem on the solutions to second-order homogeneous linear differential equations, along with a verification of the theorem on Wronskians for second-order equations. This is followed by a relatively brief discussion on generalizing the higher-order analogs of these results.
The rest of the chapter is devoted to a fairly elementary development of “linear differential operators” with some emphasis on the “factoring” of these operators. This material provides a slightly different perspective on linear differential equations, and can be enlightening to the careful. In addition, this material will make it easier to prove a few more advanced results later on in this text.
It should be noted that this chapter is more for the slightly more advanced readers who wish to see that the results in the previous chapter can be rigorously justified. The more trusting beginning readers can probably consider this chapter as optional.
