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I'm creating a course on differential equations, and I'm painfully aware that there is a LOT to teach.

As of right now, I'm considering splitting the course into two, in the following manner:

  • theory with visuals; growth models, equilibrium points (and their classifications), bifurcations, how computers solve equations (numerically)

  • strategies for solving equations by hand; separable equations, integrating factor, parameter variation, undetermined coefficients

I realize that both of these have untold depths in their own respects, but that is reasonable because since this will be a video course, I can add videos indefinitely. I might have to further split each part, but that's a problem for another day.

Question

Is this a logical way of structuring a course on differential equations into two parts?

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  • $\begingroup$ Is your course only about ordinary differential equations or does it include partial differential equations? Also, is the course for undergraduates? Are these math majors? $\endgroup$ – Joel Reyes Noche Aug 14 '16 at 1:01
  • $\begingroup$ Good question. But really, the course will be open for anyone. The videos are hosted on YouTube. So as far as the students' previous experience, I can only encourage them to do some basic calculus first (limits, derivatives, integration), and the rest is up to them. $\endgroup$ – Alec Aug 14 '16 at 1:17
  • $\begingroup$ If the course includes ODEs and PDEs, then perhaps the first video would be about ODEs and the second about PDEs. $\endgroup$ – Joel Reyes Noche Aug 14 '16 at 6:35
  • $\begingroup$ Is your question just about the division of the topics into two parts or is it also about the order in which the parts (and topics) are presented? $\endgroup$ – J W Aug 15 '16 at 6:30
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    $\begingroup$ If this is all of your structure, though, it is NOT good. Your only structure is to taking a 40 topic laundry list and dividing it into two subcategories. Instead I would think about the bare minimum AND what order to present it in. That is your core, core. And there should be some rational for order (e.g. you need to know 2nd order homo to solve 2nd order nonhomo; you need some base of general ODE knowledge before dealing with transforms or series). On top of the core, you could add * (optional) and ** (extremely optional) topics. You can even have a flow chart for pre-reqs. $\endgroup$ – guest Apr 8 '18 at 0:50

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