Against my better judgment, I have actually volunteered to teach Calculus II this semester. Sure, part of the reason is that one particularly annoying student from Calculus I did far too well last semester, and I want to make sure her ego and her spirit, is crushed this semester. But beyond that, I have decided to embrace this freshman class.
Why is that? Well, second semester calculus has a bit of a reputation among students as being the hardest math class in the calculus sequence, if not the curriculum. I suspect this is partly to do with the fact that many of the students taking this class are in the less technical BS degree programs, possibly even education, where most of the bottom of the barrel will have committed their lives. These poor souls will never know, or even probably have the ability to comprehend, the beauty in boundary value problems, measure theory, or the structure of rings and varieties.
Beyond the intrinsic mental and curriculum finality of this course, I know there are portions of it that, to the students, seem out of place among all the mechanical computation and memorization of the rest of the sequence. I speak, of course, of sequences and series. The understanding of sequences and series is absolutely essential to the entire subject of analysis, especially the underpinnings of calculus itself. Yet I know the students do their best to resist paying attention during the section on Riemann sums. I know they'll probably leave this class still trying to pretend that a capital sigma can be treated as a letter "E." But I will enjoy the look of suffering on their faces as they come to terms with the fact that they will face at least one exam consisting almost entirely of sequences and series, with almost nothing coming out to a solid, concrete answer.
Well, maybe I'll throw them a bone and give them a geometric series. Maybe even a Taylor polynomial. One with varying parameters and odd boundary behavior.
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