Calculus in 5 Hours: Concepts Revealed so You Don't Have to Sit Through a Semester of Lectures

Speak to a graph’s domain without ever using or covering end-line behavior? Extrema with no discussion of local versus global? Certainly, anyone from the point of view of “a Semester of Lectures” will be able to spot one or more things “missing” in a rapid introduction doable by lunch. Does it teach calculus? I am not sure the author is claiming anything that lofty. It does “reveal” in an orderly and cheerful fashion: pre-calculus functions review, derivatives, and integrals. Exponential and logarithm functions receive special focus, especially as inverses. Running through “Rules of Integrals” in “7 minutes” certainly does not allow time for deriving even a few of them and thus it feels more like a gallery, as is often seen pasted into the back cover of heftier calculus tomes. One area very well treated is “Geometry of Functions” as it relates to critical points, inflections, concavity and second-derivative tests. That could be a classroom capsule right there.

I would not recommend this as a replacement for a semester course, but I would recommend it for, say, someone needing to take calculus many years after their last experience. Or, someone interested but not ready to commit to a course. There could be value to follow through while one does “Sit Through a Semester of Lectures”. Exercise solutions appear on a companion site.

Tom Schulte is the math instructor for Upper Iowa University’s New Orleans Center and enjoys a twenty-mile bicycle ride and a good etouffee.