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Re: ODE's in calc II
Posted:
Mar 21, 2000 10:09 AM
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Geoff Hagopian wrote:
>The last two texts I've taught second semester calculus from have
>included a chapter on Ordinary Differential Equations.
snip
> Is
>this
>becoming a common practice? Is it good? Does it undermine or bolster the
>ODE course? Is it too shallow a treatment? It certainly seems an important
>topic for many of those majors which are not required to take ODE's as
>a separate course, but do require two semesters of calculus.
>
At Northeastern for years we included a unit on differential equations in
our first year course for engineers. This was partially because the
engineering departments did not want their students to wait until the ODE
course to see some of this stuff. it also gave us a chance to have the
students do some serious modeling using differential equations. Students
did a project on topic they were interested in which could be attacked by
first order ODEs.
I think there are a lot of advantages of mixing first order ODEs in the
calculus curriculum. It does get the students thinking about the meaning
of the derivative and the integral in a different way in the first year
courses. If you talk about exact equations in the context of gradient
fields, it adds a geometric dimension to the exact equations usually
missing from most ODE treatments. Having talked about slope fields in the
first year course, students in multivariable calculus realize quickly that
vector fields are very similar to slope fields, so it's not too surprising
that there is a connection between vector fields and differential
equations.
Pushing the "cookbook" topics into earlier calculus courses means that in
the differential equations course you can focus on topics which have more
coherence like second order equations and systems.
Best,
Terry Gaffney
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