Unformatted text preview: θ ) and − cos( θ ). Therefore 8 cos(3 t ) cos(5 t ) f ( t ) = 2 + cos( t ) − + . π 3 5 − · · · 2. When I was computing the Fourier coeﬃcients for sq( t ), I wanted to evaluate cos( nπ ) for various values of n . I started with n = 0, despite the fact that b 0 does not occur as a Fourier coeﬃcient. This was because I knew that these coeﬃcient would repeat after a while, so by starting early I would see the repetition quicker. 3. There were some questions about Fourier series for more general functions—by which I guess you meant nonperiodic functions. This is possible, but you have to use sin( ωt ) for all values of ω , not just values which are multiplies of some fundamental circular frequency. This is the “Fourier transform,” and it is closely related to the Laplace transform. 4. Some people wanted to hear more about the Gibbs eﬀect: please see the Supplementary Notes, § 16....
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 Winter '08
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 Fourier Series, Sin

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