Relearning Calculus

First, a bit of background: I took AP Calculus as a senior in high school and I earned a 5. I then spent ~20 years working as a math instructor at a community college, mostly teaching Algebra and Pre-Calculus. I never taught Calculus.

Last week, I decided to investigate how much Calculus I remembered. I checked an AP Calculus book out of the library and began to take the test. Immediately, I noticed that I used to know a lot of Calculus, but I had forgotten a lot. I knew the product rule and the chain rule, but I had forgotten the quotient rule. I knew the derivative of sine and cosine and I knew the derivative of ex. But as I continued, I realized, “Did I really know the derivative of sine?” Much of what I had remembered and even more of what I had forgotten were quick tricks. They were facts that I had memorized and certainly they were facts that had helped me pass the AP exam. But as a more sophisticated mathematician, I wanted to understand the derivative of sine, not just rotely name that it is cosine.

So I began a list. These are things I knew, but didn’t really understand. Now I want to understand.

Come with me as I embark on a journey to relearn Calculus. This time, I am looking to do much more than earn a 5 on the AP exam.