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I taught Differential Equations once back in 2006, and I am slated to teach it again this Spring. In 2006, I was assigned used Blanchard, Devaney, Hall, and I really liked this book. However, I find that it is expensive.

Now I never took Differential Equations myself, and I don't do any kind of applied math. However, from googling around a bit, I see that this may be what is called "Reform" Differential Equations, and that it emphasizes a qualitative approach. Our SLAC has no engineers, and I suspect that this would serve our students better than Boyce & DiPrima. (But I have absolutely 0 experience with the traditional approach, so I am going on a hunch).

Does any one here know of other "qualitative" Differential Equations books like Blanchard, Devaney, Hall? Perhaps even better or less expensive?

Thank you

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    $\begingroup$ Perhaps delete here and ask at: matheducators.stackexchange.com/questions $\endgroup$ – Ethan Bolker Sep 7 '17 at 13:46
  • $\begingroup$ Depending on what sort of "qualitative" view one has in mind, one might like the old book of Hirsch and Smale, or the ODE textbook of V.I. Arnol'd. Since I have no idea what an SLAC is, it's not very clear to me what sort of student you are teaching. $\endgroup$ – Dan Fox Sep 7 '17 at 14:07
  • $\begingroup$ Sorry, SLAC means Small Liberal Arts College. $\endgroup$ – Paul Sep 7 '17 at 15:53
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    $\begingroup$ What is the composition of the class? Where will they go from a Diff Eq class? $\endgroup$ – Paul Sep 9 '17 at 15:20
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"Now I never took Differential Equations myself, and I don't do any kind of applied math."

  1. I would just beware of your own blind spots. Not in math logic, but in pedagogy, application, etc.

  2. I would stick with a simple, mechanical approach to the topic. It is a very large one. Even the basic techniques can be difficult to over in a semester. Let alone approximation, computer use, transforms, etc.

  3. I would really just show them the main easy manipulative techniques (emphasis on 2nd order constand coefficient diffyQ, homo and nonhomo, that is everywhere in physics, chemistry, and engineering). Do a very quick, easy touch on the LaPlace transform (no square waves). Purpose is just an initial exposure. If they need it more in future, they learn more later.

  4. I am partial to the DiffyQ book by Sanchez. Thin, covers everything, no PDEs. But if you can't find that, consider Tenenbaum (helps the students wallets). Skip a lot of the application chapters though. [I love applications, but there is just not time; plus applications are word problems, thus hard.] Boyce and DiPrima is OK, but long and expensive.


Good luck!

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