Question: Please answer all the subquestions according to the given 1D heat equation Consider the homogeneous 1D heat equation given below Ut = Uxx Ux (0,

Please answer all the subquestions according to the given 1D heat equation

Consider the homogeneous 1D heat equation given below Ut = Uxx Ux (0, t) = 0 u(TT, t) = 0 ux, 0 =x where 0 0. (a) Find the solution to this problem using separation of variables. This includes finding any unknown coefficients present in the re- sulting Fourier series. (b) Find the associated equilibrium temperature solution, uE(x) for this problem. (c) Show that lim u(x, t) = uE(x) for this problem. 1-+ 00 (d) Calculate a bound on the error incurred by approximativex, t) by u1 ( 2, t) . (e) Use graphing software to plot the upperbound on your error in (b) and approximate the value of t for which the error is less than 10-3. (f) Draw a spatial temperature profile for this problem. g) Draw a temporal temperature profile for this

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