f(x)= modulus(x) over the interval(-pi,pi)
i have split the function into -x for (-pi,0)
and x for(0,pi)
i was wondering whether this was the right path to take i have figured out a0 to be pi
also I need a little direction on teh fourier series on f(x)=cos(ax) where a is NOT an integer therefore I am uncertain on what to do is teh question sayin a can be a rational number?
Yes, it is the right approach, and the righth value for
The reason for specifying that is not an integer is because if it is the function is aready a Fourier series (all the other terms will have zero coefficients).also I need a little direction on teh fourier series on f(x)=cos(ax) where a is NOT an integer therefore I am uncertain on what to do is teh question sayin a can be a rational number?
Yes can be rational (but not an integer, obviously), it can also be irrational.
CB
thanks very much ot both that was extremely helpful
so for the cos(ax) when i am trying to work out teh coeffiencts as cos is an even function can i conlude that the values of a0 and bn will be 0
and thus only need to figure out an
or if having to do the integration for say a0 wil is simply be 1/a*sin(ax) am i able to do this??
thanks once againfor the input it was helpful in helping me to finsh other problems i had also
You should probably disregard my last post. Here is what you should do, I think I owe it to you to show you the solution since I provided a misleading answer earlier
I will let you show which points the function
But we can say until you have shown that, that or that and have a strong correlation.
We know that the Fourier Series for on the interval is given by
Where in our specific case we have:
The last part because the integrand was odd.
So
As for your first question assuming that you mean just remember that
thank you so much and yes i didi mean that for the modulus and i had already started using that but is it possible for me to disregard a0 and an as i know that the modulus is an odd function im slightly confused because i worked out a0 using that method and obtain pi??
once again thank you so much for your help its help me understand a lot which is even better for future stuff that i will be asked to do!!!
thanks once again it was extremely helpful, i obtained for mod(x) the a_n coeff to be -2/(n^2*pi)hoever i am not sure if thsi is correct i no that there will not be any b(n) as its an even function
im not sure whether its correct or nto as for teh even and odd values i obatin the same a(n) coeff in the integral
thank you u r an absolute life saver i tried it again by myself after some long swotting and I did work it out, at the moment im trying to work out the integral for cos(ax)cos(nx)
using integration by partsi am finding to difficult therefore im going to use an identity which is cosx*cosy =1/2(cos(x-y)+cos(x+y)) and trying to integrate in this was by letting ax=x and nx=y i was wondering if thsi is the right approach to take i can see how to obtain a^2-n^" from this after all my working i get
((a+n)(a-n)(4sin(a*pi)(-1)^n))/(a+n)(a-n)
im not sure what i can do to be honest after here if you could help thanks