This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

Especially in their first upper-division mathematics courses, students often have trouble with proofs; and sometimes they object, "This is hard. I do not get it. Why am I doing this?" Though symptomatic of emotional reaction to difficulty, at its heart this is a legitimate question and it deserves a legitimate answer. This article offers one such…