>>14246763from the back matter:
This modern approach to differential equations presents the subject in terms of ideas and concepts rather than the special cases and tricks which traditional courses emphasize. No prerequisites are needed other than a good calculus course. Certain concepts from linear algebra are used throughout, but the necessary background material is given in the first chapter.
the unusual point here is that he actually means it. unlike most who proclaim that mathematical maturity be all that is needed.