APPM 4/5350 Worksheet Week 6 Figure 1: www.xkcd.com 1. Integration If you were to ﬁnd and Integrate the Fourier Cosine Series of the function in part ( a ) would you get the Fourier sine series of part ( b ) ? Explain why or why not. (a) h ( x ) = x0 < x < L (b) k ( x ) = x 2 20 < x < L 2. Complex Fourier Series Find the Complex Fourier Series for g ( x ) = ± x-L < x < 1 1 1 < x < L Write an expression relating the normal Fourier coeffecients a n and b n to the complex Fourier coefﬁent c n . (Hint: rewrite the expression f ( x ) = a0 + ∞ X n =1 ( a n cos( nx ) + b n sin( nx )) in terms of complex exponentials.) 3. Whats in a Name What does the name Gibbs have to do with Fourier Series (draw a picture)
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