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Fourier series understanding problem

  1. Dec 21, 2014 #1
    1. The problem statement, all variables and given/known data
    So the question is how does

    4/π*(sin(πx))+4/3π *(sin(3πx))+4/5π *(sin(5πx)) = 1

    for values of 0<x<1

    2. Relevant equations

    No relevant equation needed just don't understand which values of x to take.
    3. The attempt at a solution
    I am not sure which value of x to start with, it could be anything 0.1 or 0.5, how do I know which x value to start with? I have taken 0.5 and ended up with 1.05 and then taken 0.9 and ended up with 1.15. How the hell does this equal to 1 for any x value?!!!! Please help...
     
  2. jcsd
  3. Dec 21, 2014 #2
    You're missing some terms in the series, starting with the sin(7πx) term. Was there a sequence of 3 dots ... in the equation you were given? The three dots indicate an infinite series.

    Chet
     
  4. Dec 21, 2014 #3
    Yeah there were few other terms, the consecutive odd n's, I just didn't write it, sorry! and also yeah sequence of 3 dots so its infinity....but I still don't get it...can you explain how it equals 1...
     
  5. Dec 21, 2014 #4
    Are you familiar with half-wave Fourier series? Or, can you expand the following function in a Fourier series:

    y = -1 from x = -1 to x = 0

    y = +1 from x = 0 to x = +1

    Also, in terms of the series you have written, just try including more terms in the summation (say, up to 20) and see what you get when you evaluate the value at x = 0.5.

    Chet
     
    Last edited: Dec 21, 2014
  6. Dec 21, 2014 #5
    No I am not familiar with the half wave thingy. 20?! So in the exam when they ask me to do fourier sine series and show the value they converge to. I will have to write down 20 terms and then add them up? omg!
     
  7. Dec 21, 2014 #6
    I can't know what they ask you to do on your exams.

    If the question is, "how well does the three term expression you wrote match y = 1 over the interval 0<x<1?", just plot a graph of the expression as a function of x. Evaluate x every 0.05 over the interval. You can use a spreadsheet to do this type of calculation easily. Then plot the graph. I think you will be surprised at how well it fits over the entire interval with only three terms.

    Chet
     
  8. Dec 21, 2014 #7

    LCKurtz

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    More likely they are wanting you to know some of the theory about how a FS represents a function. Have you heard of the Dirichlet conditions? Do you know what the FS does when there is a jump discontinuity in the function? You don't have to literally add the series to know what the sum looks like.
     
  9. Dec 21, 2014 #8
    Nope I don't....but you could always tell me....
     
  10. Dec 21, 2014 #9

    LCKurtz

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  11. Dec 22, 2014 #10
    Can you explain page 15 please. How did ar just became 4/4 from 2/4? Because in general formula its always Ar = 2/L * etc. Secondly, how are the Ar from 2/4 equal to the one at 4/4. I don't get the integral range, like what they did in that problem
     
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