Fourier Series without complex

1. Oct 24, 2014

Alex Santos

1. The problem statement, all variables and given/known data
The problem is finding the fourier series of f(t) = e^(-t) from [0,2] where T=2 and without using complex solution.

2. Relevant equations
f(t) = a0/2 + ∑ (anCos(nωt) +bnsin(nωt)
NOT using f(t) = ∑dne^(inωt)

3. The attempt at a solution
I tried once but got completly wrong answer.
it was ∑(4*(-1)n+1*e-2+n2π2*e-2*(-1)n+1+4+n2π2) / n2π2

When I graphed this up in my texas it showed like a barcode which is definetly wrong.
When I got this solution what I did was extending the function f(t) to be even from [-2,2] and T=4 and went from there so all the bn would be equal to zero but that was as far as I got. What am I doing wrong here?

Thank you :)

2. Oct 24, 2014

vela

Staff Emeritus
One thing you're doing wrong is extending the function and changing the period. You're solving a different problem than the one that was given.

As far as your current attempt, you have no sines and cosines in your summation. That's one obvious problem. In any case, you need to show your work. Simply posting an incorrect answer is next to useless. We can't tell where you went wrong if you don't show us what you did.