Explore BrainMass
Share

Explore BrainMass

    Solve the Sine and Cosine Fourier Series and Determine the Sum of Each

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Write the cosine and sine Fourier Series. Determine the sum of each.
    { 4x 0≤x≤2
    f(x) ={ -3 2<x<4
    { 1 4&#8804;x&#8804;7

    Please see the attached file for the fully formatted problems.

    © BrainMass Inc. brainmass.com October 9, 2019, 5:32 pm ad1c9bdddf
    https://brainmass.com/math/fourier-analysis/sine-cosine-fourier-series-determine-sum-each-60232

    Attachments

    Solution Preview

    Hi again;
    (1) This part I'll repeat from last time, so that you have it with you:

    Two important functions that we'll have to integrate when we try to find the fourier coefficients are:
    xsin(kx) and xcos(kx), for some constant k.

    We can integrate these by parts, or note that:
    xsin(kx) = d/dx ( (-1/k)xcos(kx) + (1/k^2)sin(kx) )
    and
    xcos(kx) = d/dx ( (1/k)xsin(kx) + (1/k^2)cos(kx) )

    Now, for a function defined on the interval [0,2L], recall that the Fourier ...

    Solution Summary

    Sine and Cosine Fourier Series and sums are found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

    $2.19