Comment by andrepd | Hacker News Reader

Comment by andrepd | Hacker News Reader

The intention is good, but without meaning to be overly negative, this is not very well written at all. There is imprecise and needlessly confusing and unclear phrasing ("To visualize derivatives, we can draw a right triangle whose hypoteneuse [sic] is tangent to a function. If the triangle's width is , then its height is the derivative." is the most confusing and unintuitive way to visualize derivatives I can think of), a poor sequence of examples for someone who is not familiar with ODEs, plenty of things left unexplained (why do I solve \dot{y} = \cos(t) by integrating?) not to mention technical problems with hovering the graphs (at least in FF). It's also way, way too short. You simply cannot go from "an ODE is like an equation with functions and derivatives" to "let's solve one" in 5 sentences.

Honestly, reading the Wikipedia page would be more beneficial for someone who wants to learn ODEs. Like I said the intention is good but I would suggest throwing everything but the pictures away and starting from scratch, preferably with a good textbook by your side to help you not only with facts, but more importantly with the pedagogic aspect.

Eh. I have found that the Wikipedia math pages are not approachable for someone that does not already have a very strong background in math. There is definitely a place for blogs etc. that can present the information in a more palatable manner to non-mathematicians.

I also thought this was actually a nice way to think about derivatives. "To visualize derivatives, we can draw a right triangle whose hypoteneuse is tangent to a function. If the triangle's width is , then its height is the derivative." I think if it had been explained this way to me when I was first starting to learn about derivatives a million years ago, I would have grasped it more quickly.

But, I definitely agree that this is way too short for the stated purpose.

Agree, this wasn't too enlightening. I highly recommend the differential calculus course on Khan Academy. I wanted to brush up recently after having not used this stuff for over 20 years, and it was the best resource I found.

wikipedia.

Why everyone keep showering ecyclopedic knowledge on blog posts instead of updating things there?

In fairness, wikipedia does not do well for interactive content (perhaps it could?). Khan Academy is doing much better for this, but it isn't really an encyclopaedic collection of knowledge.

There really isn't a place for people to put this other than their personal blogs.

> There really isn't a place for people to put this other than their personal blogs.

That is a great idea! A place like that should exist.

> To visualize derivatives, we can draw a right triangle whose hypoteneuse [sic] is tangent to a function. If the triangle's width is , then its height is the derivative." is the most confusing and unintuitive way to visualize derivatives I can think of

This isn't only unintuitive, it's literally wrong.

No. When you first start learning about derivatives, you are told you draw a line tangent to a point and then find the slope of that line at that point. The slope is just del y / del x. So, if del x = 1, then the slope is just del y / 1 = del y = the height of the triangle.

Of course, it is more useful to get a derivative as a function of x, so you don't have to do this at every point. But, as a starting point, when you are first learning about derivatives and only have a background in algebra and geometry, this is a nice way to think about it.

Right. My browser didn't play nice with MathML, so I missed about the part where x = 1 (i.e. I couldn't see the "1" :) )

My objection was that a tangent line, as opposed to a segment, has infinite length. I can draw infinitely many segments tangent to the curve -- and get infinitely many heights for it.

Ah, ok. That makes sense. Confusion resolved!

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