In this problem we'd like to solve the boundary value problem Ə x = 4 Ə 2u
Ə t Ə x2
on the interval [0, 4] with the boundary conditions u(0, t) = u(4, t) = 0 for all t.
(a) Suppose h(x) is the function on the interval [0, 4] whose graph is is the piecewise linear function connecting the points (0, 0), (2, 2), and (4,0). Find the Fourier sine series of h(z): h(x) = - Σ bx (t) sin (nkx/4).
Please choose the correct option: does your answer only include odd values of k, even values k, or all values of k? bk(t) (16/(k^2pi^2)){(-1)^{(k-1)/2))
Which values of k should be included in this summation? A. Only the even values B. Only the odd values C. All values (b) Write down the solution to the boundary value problem Ə x = 4 Ə 2u
Ə t Ə x2
on the interval [0, 4] with the boundary conditions u(0, t) = u(4, t) = 0 for all t subject to the initial conditions u(a,0) = h(a). As before, please choose the correct option: does your answer only include odd values of k, even values of k, or all values of ? [infinity]
u(x, t) = Σ
k-1 Which values of k should be included in this summation? A. Only the even values B. Only the odd values C. All values 4 br(t) sin
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