New York University Fourier Sine Series Mathematics Questions


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1. (15 Points). Let f(x) = cosc.
(a) Find the Fourier sine series for f on the interval [0, 1].
(b) Find the Fourier cosine series for f on the interval [0, 1].
2. (15 Points). Solve the heat equation for a bar of length L = n and thermal diffusivity
k=1, with the specified boundary conditions and initial conditions
ди au
(0 < x 0) at Əx2 ди ди (0,t) (7,t) = 0 (t > 0)
u(x,0) = cos x.
(Note: You may use the results from question 1.)
3. (15 Points). Solve Laplace’s equation in the square, with the specified boundary
= 0 (0

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