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
Sapphire talk enlivens guesswork over iPhone 6
Geneticists offer clues to better rice, tomato crops
UConn makes 3-D copies of antique instrument parts
Dick
#2
Mar29-08, 11:30 AM
Sci Advisor
HW Helper
Thanks
P: 25,251
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