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okay so the reason we've been studying
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okay so the reason we've been studying
Fourier series is to essentially solve
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Fourier series is to essentially solve
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Fourier series is to essentially solve
differential equations with complicated
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differential equations with complicated
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differential equations with complicated
forcing inputs on the right hand side
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forcing inputs on the right hand side
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forcing inputs on the right hand side
which are periodic and the reason we've
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which are periodic and the reason we've
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which are periodic and the reason we've
been studying Fourier series is because
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been studying Fourier series is because
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been studying Fourier series is because
we know that differential equations with
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we know that differential equations with
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we know that differential equations with
sines and cosines as forcing terms on
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sines and cosines as forcing terms on
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sines and cosines as forcing terms on
the right-hand side are relatively easy
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the right-hand side are relatively easy
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the right-hand side are relatively easy
to solve and
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to solve and
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to solve and
we want to be able to solve the same
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we want to be able to solve the same
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we want to be able to solve the same
differential equation with a more
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differential equation with a more
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differential equation with a more
complicated periodic function on the
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complicated periodic function on the