I need to give a short presentation on introducing a class of engineering students to the concept and definition of the derivative. I'm to assume that the students are currently at the appropriate place in first quarter calculus to support the delivery. In particular, they would have been introduced to the limit, be able to compute limits for many interesting examples, had a treatment of continuity and understand what a removable discontinuity is.

So the general question here is, just take a time-tested standard treatment from a textbook, or try to do something fancier or outside the box? More particularly, introduce it as a textbook would (derive the definition and then compute examples), or jump right into computation using the definition of derivative, and then "motivate" or derive this definition?

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    This is off-topic here. Try Math Educators: matheducators.stackexchange.com – Buffy May 5 '19 at 1:04
  • didn't know about this other place to post, but thanks so much for making me down. – Nights May 5 '19 at 1:08

It would be clearer if you gave more info on your role and audience. My assumption is that you are the engineering instructor, not calculus. It sounds like they are already getting introduction to derivatives in calculus, no?

My advice would NOT be to obsess about limits and such (leave that to the formal calculus class). Keep the discussion geared to slope of a curve and some simple physical examples (position, speed, acceleration). [IOW, use of calculus in engineering.]

But again, it is hard to advise you, since you are imprecise in the question about the situation. What course are you teaching with them, are you only giving one lecture and then why the heck. What is going on in their physics classes. Etc.

EDIT: You do too know about MESE since you asked a question there on 11FEB. Maybe you aren't keeping track of the different stacks? But you have asked once before something at MESE. Note that that time, you also didn't give enough explanation of the situation.

FURTHER EDIT: And in both cases, I get impression that you are wanting to substantially remediate calculus weaknesses (for example there you mentioned topics that were too hard for weak calculus students). This is not the ideal approach. You don't have the right students for that and worse you don't have the TIME for that, with these students. You need to take much more an approach of boiling things down to the absolute most essential things. "Bang for the buck". For here, start with the simplest, most important derivatives to take. Those being speed and accelleration of a quadratic equation of position (this allows you to do gravity F=MA problems.)

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  • If I posted there, you're correct- I wasn't keeping track and had totally forgotten it existed. Frankly I feel I gave enough info here. For what it's worth, it's a one time 30-minute teaching demo. I agree with you on the level that this teaching demo is somewhat general, though I did mention engineering (not pure math) students, and in the end it shouldn't matter much for students seeing derivatives for the first time (or if it should, that's implicit in my original question). That other post you mentioned has nothing to do with this. – Nights May 5 '19 at 3:02

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