Question

Fourier Series Help!

Answer 1

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

Answer 2

what's the question?

Answer 3

Solve for 3 non zero terms

Answer 4

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

Answer 5

Yes with formulas for ao, an, bn

Answer 6

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

Answer 7

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

Answer 8

so the question is :

0 + \[\int\limits_{-3}^{-1} (an \cos n x + bn \sin nx) dx \] for the first term right?

Answer 9

let me look

Answer 10

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

Answer 11

for the second term.

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

Hmm alright. Thanks

Answer 20

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)

Answer 21

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

Answer 22

A little :) Thanks

Answer 23

lol, np ^_^ good luck.