1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the Fourier series of a function.

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data
    f(x)=
    -cos(x) when -π<x<0
    cos(x) when 0<x<π

    Decide if f is an even, odd function or either.
    Find the Fourier series of f.

    2. Relevant equations

    odd function: f(x)=f(-x)
    even function: -f(x)=f(-x) or f(x)=-f(-x)

    3. The attempt at a solution

    substitute -x into either cos(x) or -cos(x) => -cos(x)=-cos(-x) and cos(x)=cos(-x),
    therefore, f is an even function.

    However, I'm stuck when it comes to finding the Fourier series.

    I know how to solve a0, where I just need to find the integration of -cos(x)dx and cos(x)dx. To find an and bn, I need to find the integration of [-cos(x)cos(nx)dx], [cos(x)cos(nx)dx], [-cos(x)sin(nx)] and [cos(x)sin(nx)dx]. I tried to solve them using integration by parts, but it turned out to be infinitely expanding, so I guess integration by parts won't work. Is there any other way to integrate the above four functions?
     
  2. jcsd
  3. Dec 7, 2011 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Your definitions of "even" and "odd" are the exact opposite of everybody else's in the world.

    RGV
     
  4. Dec 7, 2011 #3

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You need the product formulas:

    http://www.sosmath.com/trig/prodform/prodform.html
     
  5. Dec 7, 2011 #4
    I just typed it wrong but they wouldn't let me edit it. :(
     
  6. Dec 7, 2011 #5
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook