Question

f(x)= -1 if -pi 15 years ago

Answer 1

f(x) has period of 2pi

Answer 2

Find Fourier Series

Answer 3

You want to create a function:
\[f(x) = a_0+a_1\cos(x)+b_1\sin(x)+a_2\cos(2x)+b_2\sin(2x)+\ldots\]
the formula for the a's is:
\[a_n = \frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\cos(nx)dx\]and the formula for the b's is:
\[b_n = \frac{1}{\pi}\int\limits_{-\pi}^{\pi}f(x)\sin(nx)dx\]

ima do the calculations on paper, i hate typing integrals in latex >.>

Answer 4

Thanks Joe, I am gonna print those out and try to figure it out

Answer 5

first one finds a_n , second finds b_n , what does third one do?

Answer 6

here is what the function looks like with the first couple of terms, you can see it starting to form the function (although it would take quite a bit of terms to make it look better)

http://www.wolframalpha.com/input/?i=%284%2F%28pi%29%29sin%28x%29%2B%284%2F%283pi%29%29sin%283x%29%2B%284%2F%285pi%29%29sin%285x%29%2B%284%2F%287pi%29%29sin%287x%29%2B%284%2F%289pi%29%29sin%289x%29%2B%284%2F%2811pi%29%29sin%2811x%29%2B%284%2F%2813pi%29%29sin%2813x%29%284%2F%2815pi%29%29sin%2815x%29

Answer 7

third is the finish of the b_ns

Answer 8

oh, okay