My Calc III final was today, and after spending the weekend at my office reviewing my notes and doing problem after problem, I was as ready as I would ever be.
You name it, I had probably done a problem (or two or three) on it. Double and triple integrals, cartesian, polar, cylindrical and spherical coordinates, mass, moments, centroids and density, reversing the order of integration, Riemann sums, to name just a few of the topics that would be on the test.
And when I sat down to take the test this morning, I paged through it and felt confident. At least this time I recognized most of the problems.
But as I was to find out after the test, sometimes the devil is in the details, or to use a sport analogy, it’s all about the blocking and tackling.
There was one problem that required some calculus, and I’m fairly certain I did it correctly until I got to the end, and something about the answer just did not make sense.
When I turned in my test, I asked my teacher about it, and he took a quick glance at it. Everything was good until the end, at which point I had to evaluate a fraction conceptually similar to the following:
For whatever reason, I decided to split this into two separate fractions, as follows:
1 + 1
The teacher said something like, “You can’t do that” (while somehow keeping a straight face), and before he had finished the sentence, I saw my mistake.
Of course you can’t do that. I learned that in probably third grade, and it was probably reinforced every year for the next nine years of school.
It was a careless mistake, and fortunately this time there were no serious consequences (except my brooding over it for the rest of the day).
Maybe it was because my blood sugar level was running a little low after a couple of hours of doing calc problems; I’m just not me (or my third grade me) when I’m hungry.
But it’s over for now, and I am looking forward to doing lots and lots of reading and relaxing over the next couple of weeks.
There’s also a lesson here somewhere; something along the lines of:
Me, in third grade: “This fraction stuff is useless; I’ll never need to use this again…”