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## anonymous 5 years ago Fourier Series Help!

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1. anonymous

$f(x)= 0 -3\le x<-1, 3 -1\le x < 1, 0 1 \le x < 3$

2. anonymous

what's the question?

3. anonymous

Solve for 3 non zero terms

4. anonymous

remind me, we have to integrate between these points, right?

5. anonymous

Yes with formulas for ao, an, bn

6. anonymous

$f(x) = a0 + \sum_{n=1}^{\infty}(an \cos nx +bn \sin nx)$

7. anonymous

Not familiar with it in that form but it looks similar yeah

8. anonymous

so the question is : 0 + $\int\limits_{-3}^{-1} (an \cos n x + bn \sin nx) dx$ for the first term right?

9. anonymous

let me look

10. anonymous

then 3 - (the integral between -1 and 1) , right?

11. anonymous

for the second term.

12. anonymous

$ao= 1/2L \int\limits_{-L}^{L} f(x) dx$

13. anonymous

$an= 1/L \int\limits_{-L}^{L} f(x)\cos* n \pi x/L dx$

14. anonymous

lol, yes! For the first one the interval is between [-3,-1) so you'll integrate and get the following form:$= \int\limits_{-3}^{-1}a0 dx + \int\limits_{-3}^{-1}\sum_{n=1}^{\infty}(an \cos nx + bn \sin nx)dx$

15. anonymous

That is for solving a0 right? I'm not used to seeing sigma or it done with all the integrals combined.

16. anonymous

$=2 a0 +\sum_{n=1}^ {\infty} an \int\limits_{-3}^{-1} \cos nx dx + \sum_{n=1}^{\infty}bn \int\limits_{-3}^{-1}\sin nx dx$

17. anonymous

lol, that's the general form of fourier's series ^_^

18. anonymous

then you can integrate cos nx and sin nx and treat n as csts :), then you'll get the answer

19. anonymous

Hmm alright. Thanks

20. anonymous

separate them and solve each one alone then combine them and you'll get: $\int\limits_{-3}^{-1}\cos nx dx$ and then integrate : $\int\limits_{-3}^{-1}\sin nx dx$ find the answer and combine it with : = 2ao + _____ + _____ ( the answers you'll get after integrating)

21. anonymous

same thing goes with the other zeros ^_^ good luck! hope I made it easier for you :)

22. anonymous

A little :) Thanks

23. anonymous

lol, np ^_^ good luck.

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