3 ms·

This is what I tend to struggle with when reading maths textbooks. Example from your page: Sup­pose that you monitor the file size dur­ing the en­tire down­lo

• ivan_ah 13y ago
  I understand your unease. In this case I totally pulled this equation f(t)=0.002t^2 out of nowhere. It is just "some" function that satisfies f(0)=0 and f(600sec)=720MB. I basically skipped (invented) the modelling step. In practice you would observe the download size f as a function of time t, and then ask yourself "which function f(t) correctly describes what I see." I wanted to describe a download that gets faster and faster with time, so I picked a quadratic function f(t)=At^2 as a template, then chose A=0.002 so the function matches the problem statement. Suppose instead I wanted the download rate to be uniform (constant download speed), then the function which describes the file size would be of the form f(t) = mt+b. More specifically, the function would be f(t)=720/600t+0=1.2t. (You can check that f(0)=0 and f(600)=720, as in the problem setting). In general, once you become familiar with the main function families f(t)=mx+b, f(t)=ax^2+bx+c, f(t)=Aexp(kx), f(t)=ln(x), f(t)=Asin(kx-ϕ), etc, you will be able to describe real-world phenomena by using one of these equations. This ability to "model" the real world through mathematical equations is one of the super-powers that comes with math knowledge, but my download example doesn't quite manage to communicate that. I will have to rework it... For a slightly better example of "modelling" using equations, check out page 26 in the PDF preview: http://cnd.mcgill.ca/~ivan/miniref/miniref_v4_preview.pdf#page=26 http://cnd.mcgill.ca/~ivan/miniref/miniref_v4_preview.pdf#pa...