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Comment by chrstphrhrt | Hacker News Reader

Which order were they taught in?

I had the same curriculum but was utterly bewildered by derivatives being the first topic. For the simple reason that until that point I had habitually looked at "wholes" in the external world, only then to wonder "what kinds of things progressively make it up?"

I feel like to derive something, you start with the assumption that you know what you're talking about fist. Yet the thing is actually the sum of its parts. Therefore integration seems more natural at first, and only then can things similar to it be derived with confidence.

So the teaching order seemed backwards. I wonder if anyone has felt the same way.

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Every school I've ever been at in British Columbia (High School, College, University) - starts with derivatives, and then moves onto integral calculus.

They start with the calculating slope on a curve f(x) being lim h->0 f(x+h)-f(x)/h - spend a few weeks deriving various derivatives, show how you can find tops/bottoms of curves (derivate=0), talk about limit theory a bit, take a bunch more complicated equations derivatives.

Then, once that's figured out - take the inverse, and look at area's under curves, volumes, etc... My brain lost it at integration by parts (so many parts) - too much memorization, and so came an end to my mathematics education in that space.

I'm happy they were taught in that order, mostly on being exasperated with having to memorize all the integration by parts formulas.

Thankfully, you don't have to remember the integration by parts formula, just the usual derivative of a product and rearrange.

Yep! Archimedes was essentially doing integrals 2000 years ago. He got close to infinitesimals, and centuries later we had derivatives and limits. It's strange to teach them in the reverse order (i.e. Most sophisticated theory first, like teaching the reals before the integers).

I have an online series that starts with the historic order which you might like:

http://betterexplained.com/calculus/lesson-1

Thanks!

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