Question: Problem 2 (30 points) Consider the function f(a:) = 1:2 over the interval 0 S a: g 1. (a) (8 points) Derive the Fourier sine

Problem 2 (30 points) Consider the function f(a:) = 1:2 over the interval 0 S a: g 1. (a) (8 points) Derive the Fourier sine series over the interval 0 g a: g 1. (b) (8 points) Derive the Fourier cosine series over the interval 0 g a: g 1. (c) (8 points) Derive the full periodic series over the interval 0 g :c g 1. (d) (6 points) For each of the series above determine the location(s) of the Gibbs phenomenon (if any)

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