The purpose of this companion volume to our text is to provide
instructors (and eventu- ally students) with some additional information
to ease the learning process while further documenting the
implementations of Mathematica and ODE. In an ideal world this volume
would not be necessary, since we have systematically worked to make the
text unambiguous and directly useful, by providing in the text worked
examples of every technique which is discussed at the theoretical level.
However, in our teaching we have found that it is helpful to have
further documentation of the various solution techniques introduced in
the text. The subject of differential equations is particularly
well-suited to self-study, since one can always verify by hand
calculation whether or not a given proposed solution is a bona- fide
solution of the differential equation and initial conditions.
Accordingly, we have not reproduced the steps of the verification
process in every case, rather content with the illustration of some
basic cases of verification in the text. As we state there, students are
strongly encouraged to verify that the proposed solution indeed
satisfies the requisite equation and supplementary conditions.