Ordinary Differential Equations Homework 5 Solution

Fourier Series:


    1. Section 33: Problem 1, 7

    2. Section 34: Problem 5 Add this as part d: To what value does the series converge at the points of discontinuity?

    3. Section 35: Problem 8 Do not use the Fourier series you derived to sketch the Fourier series.

    4. Section 35: Problem 3

    5. Suppose f is a piece-wise continuous function on [0, π] such that f(θ) = f(π − θ). (That is, the graph of f is symmetric about the line θ = π/2.) Let an and bn be the Fourier cosine and sine coefficients off. Show that an = 0 for n odd and bn = 0 for n even.























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