APPM 4/5350 Worksheet Week 6Figure 1:www.xkcd.com1.IntegrationIf you were to find and Integrate the Fourier Cosine Series of the function in part(a)would you get theFourier sine series of part(b)? Explain why or why not.(a)h(x) =x0< x < L(b)k(x) =x220< x < L2.Complex Fourier SeriesFind the Complex Fourier Series forg(x) =x-L < x <111< x < LWrite an expression relating the normal Fourier coeffecientsanandbnto the complex Fourier coeffientcn.(Hint: rewrite the expressionf(x) =a0+∞Xn=1(ancos(nx) +bnsin(nx))in terms of complex exponentials.)3.Whats in a NameWhat does the name Gibbs have to do with Fourier Series (draw a picture)
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