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Rifled through it, seems to be just the standard stuff. I was particularly disappointed by: > The bad news is that this is a little harder than using the Monk
by norswap 7y ago
Rifled through it, seems to be just the standard stuff.
I was particularly disappointed by:
> The bad news is that this is a little harder than using the Monkey Rules to calculate derivatives. In some sense the Monkey Rules, particularly the Quotient Rule and the Chain Rule, "blow functions up" when they systematically calculate derivatives. In order to go backwards, and undo the Monkey Rules to find antiderivatives, you need to think a bit like a forensic analyst who studies the site of an explosion to see what sort of bomb was used. We'll discuss this analogy more later when we practice finding antiderivatives.
("Monkey rules" are the derivation rules, this kind of cuteness is a big part of the purported dumbing down)
Anyway, systematically calculating derivatives was always a big sticking point for, as indeed you often need to use multiple rules and it's not quite obvious which chaining of rules will get you there. I was hoping the authors could introduce a systematic algorithm (which no doubts exists but I never bothered looking up - I don't do much integrals day to day) or at least some strong form of intuition that goes beyond "if we did this we'd have something on which we could apply that rule".
- gregpetrics 7y agoGood feedback. I struggled with deciding if I should write activities that illustrate the full algorithm for derivatives and antiderivatives. At this time I left it out, but I do have the materials... The book was written with a bit of a promise to keep the algebra out, and overdoing it on Monkey Rules (derivatives) and Lucifer's Rules (antiderivatives) breaks that promise. That said, calculating derivatives and antiderivatives is the fundamental algebraic task of a calculus student. I'm thinking about your feedback right now... and will likely make adjustments in the near future to introduce optional tracks for extra practice on this.
- norswap 7y agoThat's great to hear :)