How to solve fourier series integrals

Thread Starter

gutto@Mac

Joined Nov 26, 2007
1
Ive tryin to solve the fourier series integrals but they are really confusing.....
when we find "an" and "bn" we solve integrals how do we solve them completely to get the answer...my book has only shown the an formula deivation and then it says
"by long integration we got following answer...."
Any tips on that

Papabravo

Joined Feb 24, 2006
16,523
There are two tools that are handy in integration:
1. Integration by Parts
2. Trigonometric Identities
My favorite is
cos(n+1)θ + cos(n-1)θ = 2cos(θ)cos(nθ)

mogadeet

Joined May 1, 2007
19
hey gutto

the proof in your book isn't exactly incomplete: phoned-in, maybe. the thing is, the derivations for the sine coefficients and for the cosine coefficients are formally almost identical. the only difference is the obvious one (one talks about the sine function while the other talks about the cosine function). try adapting the proof you've got in the most obvious way and see if it doesn't work. i threw out my notes on this but i can puzzle it out again if you're really curious.

peace
stm