Explore BrainMass

Explore BrainMass

    Fourier Series and Fourier Sine and Cosine Series

    Not what you're looking for? Search our solutions OR ask your own Custom question.

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

    1.) Find fourier series of f(x)=4, x greater than -3 and less than 3

    and

    2.) Find fourier series of f(x) = x^2-x+3, x greater than -2 and less than 2

    and

    3.) Write the cosine and sine fourier series f(x)=x^2 for x greater than 0 and less than 2

    © BrainMass Inc. brainmass.com September 26, 2022, 9:55 am ad1c9bdddf
    https://brainmass.com/math/fourier-analysis/fourier-series-fourier-sine-cosine-series-60184

    Attachments

    Solution Preview

    For a function periodic on an interval instead of , a simple change of variables can be used to transform the interval of integration from to . Let

    (11)

    (12)
    Solving for gives , and plugging this in gives

    (13)
    Therefore,

    (14)

    (15)

    (16)

    1. , ...

    Solution Summary

    Fourier Series and Cosine and Sine Fourier Series are found. The solution is detailed and well presented.

    $2.49

    ADVERTISEMENT