Jerry Rosen recently posted a list of what he perceives to be deficiencies he finds in the Harvard Calculus text (HC).
I should like to shift the discussion from HC, which I think that Jerry mistakenly uses to epitomize a monolithic reform that simply does not exist. Therefore, instead of addressing Jerry's deficiencies in the context of HC, I will discuss the way in which *this reformer* believes we should handle those things in our calculus courses.
Jerry's list (which I will not re-post, in order to keep message lengths within reasonable bounds) can be broken down into four distinct classes: Underemphasis on Algebra (which is item 7), into which I place also partial fractions (item 12) and related rates (item 14); Missing, Defective, or Inappropriate Definitions [exponentials & logs (3), limits (13), continuity (15), and the Riemann integral (16)]; Missing, Defective, or Inappropriate Theory [the Quotient Rule (4), the Intermediate Value Theorem (7), differentiability implies continuity (8), the Mean Value Theorem and its consequences (9)]; and Un-, or Inappropriately Treated Topics [convergence tests for series (5), L'Hopital's Rule (6), polar coordinates (10), parametric equations (11)].
Jerry has also complained that HC is a poor reference. I have addressed that complaint elsewhere, and I will not repeat those remarks.
Because Jerry's list is long and I have much to say, I will distribute my remarks through a series of shorter notes. Those who, for whatever reason, don't want to plow through them can delete them without much pain.