[Blindmath] Basic mathematical concept question
David Tseng
davidct1209 at gmail.com
Sat Mar 24 19:30:05 UTC 2012
With regard to accessible materials I would start with seeking a
non-lossy medium for your textbook. When I went through my
undergraduate work in mathematics, I employed a variety of techniques
to accomplish this. If you can find it, audio recordings of Calculus
books (Stewart comes to mind) are available in the U.S. Despite the
very sequential (tape) nature of this method, humans reading the book
render the text precisely and insert appropriate descriptions for
figures/graphs when appropriate. This becomes invaluable as you move
through Calculus in its differential, integral, and multi variable
variants.
There are also now Daisy equivalents of the above. So, you can
download an audio book that has chapter/section indecies.
Alternatively, you can try to have relevant materials hand-annotated
by whatever resources your college may offer.
Finally, wikipedia, though it reads more like a reference than say a
tutorial, is quite accessible. Images have alt tags that expose the
raw LaTeX of the expression under discussion.
Hth,
David
On 3/24/12, Andrew Stacey <andrew.stacey at math.ntnu.no> wrote:
> That was a nearly perfect explanation.
>
> Just one small technicality. The properties that Richard refers to as
> "continuous" and "discontinuous" are actually "differentiable" and
> "non-differentiable". The rough-and-ready description of a function being
> continuous is that its graph can be drawn without taking the pencil off the
> paper. The actual definition is a little more complicated, but that's the
> basic idea. A continuous function has no jumps, no gaps. It is
> a differentiable function that has a well-defined slope everywhere.
>
> A differentiable function is automatically continuous, but not vice versa.
>
> Some examples:
>
> 1. A discontinuous function: define f(t) = 0 if t < 0 and f(t) = 1
> otherwise.
> This has a jump at 0 so is discontinuous.
>
> 2. A continuous function that isn't differentiable: f(t) = 0 if t < 0 and
> f(t)
> = t otherwise. This is continuous, but it has no well-defined slope at
> 0 since as we approach 0 from the left the slope appears to be 0 (flat)
> whereas if we approach it from the right then the slope appears to be 1.
>
> Most functions that you encounter are differentiable, in fact probably even
> better than that. But properly defined, most functions that exist are not
> differentiable anywhere. It's just that since differentiable functions are
> so
> easy to study (compared to arbitrary functions), we use them if at all
> possible.
>
> Andrew Stacey
>
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