These notes are based on lectures given by the first author to students in the course on elementary differential equations over many years, and have been
extensively class tested. They can be used as a stand alone text or as supplement to a standard text. Our aim
is to make the subject more interesting by avoiding the usual labor intensive methods in favor of more powerful and elegant methods such as the well known operator methods, rarely described in standard texts. Another example is the use of Leibniz's theorem in power series
solutions. We include many applications and plenty of exercises.
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