Finding the Fourier Series: A Beginner's Guide

[briteliner]

Homework Statement

find the Fourier series for the function

0 -pi<x<pi
f(x)={
sinx 0<x<pi

Homework Equations

The Attempt at a Solution

I don't know how to do this and can't find a good explanation anywhere, any kind of help is appreciated...even just a push in the right direction

 

[Dr.D]

Are you saying your function is
f(x) = 0 x<-pi
= sin(x) 0<x<pi
= 0 x>pi
If so, that is not periodic and does not have a Fourier series in the usual sense, although it probably has a Fourier transform. Is that what you want?

 

[briteliner]

we are supposed to assume that the function is continued outside of the interval with period 2pi periodically.
i just realized there was a mistake with the bounds also, but i fixed it now. it is a piecewise function which equals 0 from -pi to pi and sinx from 0 to pi

 

[Dick]

I'm going to guess that the problem is to find the Fourier series on the interval [-pi,pi] of the function f(x)=sin(x) for x in [0,pi] and f(x)=0 for x in [-pi,0]. If so, then the coefficients of that series are defined in terms of integrals of sin(x) times sin(nx) and cos(nx). Since f(x)=0 for x<0, just integrate from 0 to pi. Can you do any of them?

 

[briteliner]

ok thanks so then i have integral from 0 to pi of sinxcosnx dx. would this just give 0 since sinx is odd and cosnx is even, giving an odd function?

 

[Dick]

You are only integrating over [0,pi]. Oddness or evenness doesn't help. And you also need to integrate sin(x)*sin(nx). Use trig product to sum formulae. Like at the bottom of this page. http://www.sosmath.com/trig/Trig5/trig5/trig5.html

 

[briteliner]

oh right. thanks so much!