Calculus INB – Optimization and Integration

Seniors leave early due to graduation every year in May. With the seniors, we made it through Optimization…and then spent some time on a project optimizing boxes and cans. Maybe I’ll have some time later to post about that. With three juniors, we finished up the year learning about differentials, linearization and integration. The topics don’t necessarily lend themselves to being a unit…but hey, it’s the end of the year!

Optimization was pretty much done like I did first semester, so I won’t bore you too much with those details. Integration was done in a similar fashion as that post too, though I had some time to use rectangular approximation to introduce the topic, which I did not have time for first semester due to the crazy amount of snow days we had.

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Newton’s Method: File-25-06-2014-10-39-20 A neat topic to spend a short amount of time on, relating how these numbers were approximated before the advent of graphing calculators and computers. It’s really amazing how close these approximations were so long ago!

Optimization Files

Differentials Files

Integration Files

Optimization and Integration

After getting back to business from the holiday break and many snow/cold days, my students were ready to be done with Calculus (block schedule means classes are only a semester, then all new classes). Administration decided to push back exams a week to allow for enough time to go through the curriculum. I was ok with it either way, but it gave us a chance to get through some optimization problems in calculus, as well as introduce Integration. Coming back to school on a Thursday, a week after we were supposed to return from break, I was very happy that I had planned for some activities for the students to do. Last year I found the following introduction to optimization activities online (sorry, I cannot remember where!). They are nice because they work students through doing them by creating objects, doing the algebra and finally calculating with calculus. It gives the students a visual to think about later.

Introduction to Optimization

We then spent a few days working on example problems and worksheets. Here are my INB pages:

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I particularly enjoyed the notes on the pink paper. They actually created shapes that were being described in the problems.

The extra few days of the term allowed for me to introduce the integral, or the anti-derivative. We just went through the basics, what it is, how to use the power rule. Two days does not allow for a lengthy, in-depth conversation about it. Some years we have more time spent on integrals, other years we don’t even get to them.

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