Fourier Series question

[math_04]

I can do the Fourier series but this question is really confusing

F(x) is 1 for 0<x< pi , 0 for pi < x < 2pi and f(x+2pi) = f(x) for all x

I know that it means that the period is 2pi and L = 2pi/2 = pi

1) Sketch f(x) for -4pi <x < 4pi

I sketched the graph so that is alrite

2) Find the Fourier series for f(x)

This is where it gets confusing. What is f(x)?? what is the function? Is it a unit step function or what?

Thanks.

[CompuChip]

F(x) is 1 for 0<x< pi , 0 for pi < x < 2pi and f(x+2pi) = f(x) for all x
I assume that in the first part, you meant to write f(x) instead of F(x). Also the function is now undefined at x = 0, 2 pi, 4 pi, etc., so you may want to include something like: f(0) = 1/2, in the definition.


2) Find the Fourier series for f(x)

This is where it gets confusing. What is f(x)?? what is the function?
I assume this is part b) of the same question, so my guess is they mean the same function you defined above and you have graphed in 1).

[math_04]

1. The problem statement, all variables and given/known data

I can do the Fourier series but this question is really confusing

F(x) is 1 for 0<x< pi , 0 for pi < x < 2pi and f(x+2pi) = f(x) for all x

I know that it means that the period is 2pi and L = 2pi/2 = pi

1) Sketch f(x) for -4pi <x < 4pi

I sketched the graph so that is alrite

2) Find the Fourier series for f(x)

This is where it gets confusing. What is f(x)?? what is the function? Is it a unit step function or what?

Thanks.


2. Relevant equations

Euler coefficient equations.



3. The attempt at a solution

I can do the solution but I have no idea what f(x) is!

[malawi_glenn]

"F(x) is 1 for 0<x< pi , 0 for pi < x < 2pi and f(x+2pi) = f(x) for all x"

you mean:

f(x) is 1 for 0<x< pi , 0 for pi < x < 2pi and f(x+2pi) = f(x) for all x
??

the last statement, f(x+2pi) = f(x), mean that the periodicity of the function is 2pi.

So when doing the fourier series, you only need to know the period and what the function looks within that intervall.

The function f(x) is 1 for 0<x< pi , 0 for pi < x < 2pi, 1 for 2pi < x < 3pi, 0 for 3pi < x < 4pi etc.

[math_04]

But u see how do u integrate that as a function.

You cant put o< x <1 in an integral and integrate right? You see what i mean? I want to know how you right that in a form in which you can integrate.

And yea what you have written is right.

Thanks.

[math_04]

i mean 0 <x < pi and integrate. And you need to know what L to solve a Fourier Coefficient. L is Period/2

[HallsofIvy]

Suppose f(x) were x2 from 0 to 1 and 2x from 1 to 2. How would you integrate f from 0 to 2? Realizing that the integral of such a function is just the area under the curve, you should also realize that you can find the area of each part and then add. That is, you integrate the x2 from 0 to 1, its domain of definition, and integrate 2x from 1 to 2.