Register to reply

Fourier series and even/odd functions

Share this thread:
Niles
#1
Mar29-08, 11:03 AM
P: 1,863
1. The problem statement, all variables and given/known data
I found the solution to a PDE in this thread: http://www.physicsforums.com/showthread.php?t=224902 (not important)

The solution is the sum of u(rho, phi) = [A_n*cos(n*phi)+B_n*sin(n*phi)]*rho^n.

I have to find the general solution, where rho=c, so I equal rho = c, and I am told that u in this point equals sin(phi/2) when phi is between 0 and 2*pi.

I must find the Fourier-coefficients (since it is a Fourier-series).

My questions are:

Since sin(phi/2) is an ODD function, can I discard A_n and just find B_n? That is what I would do, but in the solutions in the back of my book they find A_n as well. Why is that?! The book even says that for an odd function, the Fourier-series only contains sine, so A_n can be discarded, but they still find it. Can you explain to me why A_n must be found as well?
Phys.Org News Partner Science news on Phys.org
Fungus deadly to AIDS patients found to grow on trees
Canola genome sequence reveals evolutionary 'love triangle'
Scientists uncover clues to role of magnetism in iron-based superconductors
Dick
#2
Mar29-08, 11:30 AM
Sci Advisor
HW Helper
Thanks
P: 25,228
The integral of an even function times and odd function will generally vanish only if you are integrating over an interval symmetric around the origin, like [-L,L]. Your interval here is [0,2pi]. The A_n's don't automatically vanish.
Niles
#3
Mar29-08, 11:31 AM
P: 1,863
Ahh, I see.

You have helped me very much lately. Thank you.


Register to reply

Related Discussions
Need help to find application of the Fourier series and Fourier Transforms! Introductory Physics Homework 8
Fourier Series Precalculus Mathematics Homework 23
Fourier series Calculus & Beyond Homework 17
Rom fourier transfom to fourier series Calculus & Beyond Homework 1
Fourier Series / Fourier Transform Question Electrical Engineering 6