Mathochism: Simple, explicit and normal

One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?

Under the compass of Damocles I may have had a hell of a time recognizing disguised absolute values in limits, but I’m actually doing okay on derivatives.

I suppose that is because the calculus part is actually very brief — it’s mostly algebra and trig, and I’m quite solid on those. It’s also wonderfully fiddly, as long as I stay organized.

Then again, aren’t derivatives a huge part of calculus? I mean, instantaneous rate of change, acceleration, etc.? You can’t calculate that in plain algebra or geometry, right? So I am doing actual calculus? *Bounces up and down excitedly*

Anyway, the chain rule feels less intimidating this time, although I’m not consistently simplifying the way the book wants me to. I’m still befuddled on what calls for total versus partial simplification. It seems arbitrary. Perhaps some of the instructors out there can enlighten me?

Another question: Does anyone know why lines perpendicular to the tangent line are referred to as “normal”? I asked that question in class, but the prof didn’t know the origin. A classmate who is studying physics said it may have to do with the Latin word for square, but I can’t seem to find anything about that elsewhere.

As a writer, especially one for whom English is a second language, I find how the meaning of words changes depending on context fascinating. Who would have thought “normal” in math means perpendicular?

Also, we’ve been working on implicit differentiation (talk about fiddly!), and the professor told us about the difference between explicit and implicit approaches.

I can’t help myself — when I see the word “explicit,” my mind goes to sex. I blame Tipper Gore; I was a teen when her campaign against racy lyrics began. Sadly, explicit differentiation isn’t that sexy. (Even if a function has to be smooth at the differentiable point.)

Implicit differentiation doesn’t cause pants feelings either (and I tend to associate the word with judgyness — what is that derivative implying?), but I do find it kind of fun.

Now, I have to go practice. I am hoping my comfort with derivatives will spill over on the test. It’s next week, and I’d just like to pass this one!

All text copyrighted by A.K. Whitney, and cannot be used without permission.

5 comments

  • In calculus classes I recall the rule on simplification was to never simplify your final answer because you’ve already done the calculus part so you’re solved the problem and the simplification step is just an opportunity for mistakes. Of course that depends on what your professor actually asks for. Simplification is useful for understanding the solution and for making an expression easier to work with in a future step (e.g. when computing a double derivative, you usually compute the single derivative and then simplify before differentiating a second time).

    As someone used to technical discussions with jargon, I enjoy having it pointed out how weird it sounds (this gets quite silly in board game rule discussions sometimes). It had honestly never occurred to me to wonder where “normal” came from. Now I’m going to check back to see if you find an answer.

  • According to the Oxford English dictionary, the English world “normal” is derived from the Latin word “normalis” meaning right-angled.

  • Thank you, Bill! That makes sense.

  • Have you seen khanacademy.org?

  • I have. Great site.

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