Question: Problem 5 (Fourier series, Haberman Chapter 3, sections 3.1-3.3) (a) Find the Fourier sine series of the constant function f(x) = 1 on the interval

Problem 5 (Fourier series, Haberman Chapter 3, sections 3.1-3.3) (a) Find the Fourier sine series of the constant function f(x) = 1 on the interval of interest (0, L). (i) Describe the convergence of the series expansion from part (a). (ii) Take L = 1, and if Gibb's phenomenon is present, verify it numerically. (b) Find the Fourier cosine series of the constant function f(x) = x on the interval of interest (0, L). (i) Describe the convergence of the series expansion from part (b). (ii) Take L = 1, and if Gibb's phenomenon is present, verify it numerically. (c) Find the full Fourier (sine and cosine) series of the constant function f(x) = x] on the interval of interest (0, L). (i) Describe the convergence of the series expansion from part (c). (ii) Take L = 2, and if Gibb's phenomenon is present, verify it numerically

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