Question

(PDE)(Periodic Functions) I'm having trouble understanding what you can and cannot do in the argument of a periodic function after having made a change of variables, more info below.

Answer 1

http://see.stanford.edu/materials/lsoftaee261/Midterm-2006-Solutions.pdf

In the solution to Example 1, I'm confused about this part: http://i.imgur.com/zFA084u.png

Does this imply that, say I have some function \[\alpha(x)\] that I know to be periodic of period P, say it's almost exactly like this posted problem and you have the original function...give me a minute.

Answer 2

@Kainui I dunno, I'm having trouble phrasing my question, but I'm wondering whether I had some periodic function of a known period as the integrand of a given integral, and I made up some other function that is for substitution...

Answer 3

Yeah, all the period means is that it's exactly the same function again after that point. Just like sine and cosine have period of 2pi. \[\Large \sin(x)=\sin(x+2\pi)\] You could continually do this actually and it wouldn't matter, \[\Large \sin(x)=\sin(x+n2\pi)\]