How Diff. Ranges Affect Fourier Series

[jegues]

Homework Statement

I just have a general question about a set of questions given in my textbook.

Homework Equations

The Attempt at a Solution

The questions are given in sequential order, and they both ask the same thing,

Find the Fourier series of the function f(x).

One question gives,

$$f(x) = 3x, \quad 0 < x \leq 2L, \quad f(x+2L) = f(x)$$

The question immeadiatly after gives,

$$f(x) = 3x, \quad -L < x \leq L, \quad f(x+2L) = f(x)$$

Note that the only thing that changed in these two questions was the range in which the function is defined.

How is this difference in range, or where the function is defined going to affect the resulting Fourier series?

Is there an obvious conclusion I should be drawing from this?

Thanks again!

 

[LCKurtz]

They are two different functions (draw more than one period). Look at their graphs. For example, the second one is an odd one and the first isn't. You will get completely different series.