Two straight, thin rods of length 1m each, made from the same material are joined at...

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Two straight, thin rods of length 1m each, made from the same material are joined at one end and the resulting rod is insulated completely. At the moment they were joined (t = 0), one of the rods had a constant temperature of -1°C, while the other had a constant temperature of 3°C. The thermal diffusivity constant for the material used is 9. (a) (4 points) Write down an initial-boundary-value problem whose solution u(x, t) represents the temperature in the rod at location 0 < x < 2 and time t > 0. (b) (5 points) Extend the initial data to an odd periodic function and write down the Fourier sine series associated to it. (c) (6 points) Determine the temperature u(x, t) at location 0 < x < 2 and time t > 0. Two straight, thin rods of length 1m each, made from the same material are joined at one end and the resulting rod is insulated completely. At the moment they were joined (t = 0), one of the rods had a constant temperature of -1°C, while the other had a constant temperature of 3°C. The thermal diffusivity constant for the material used is 9. (a) (4 points) Write down an initial-boundary-value problem whose solution u(x, t) represents the temperature in the rod at location 0 < x < 2 and time t > 0. (b) (5 points) Extend the initial data to an odd periodic function and write down the Fourier sine series associated to it. (c) (6 points) Determine the temperature u(x, t) at location 0 < x < 2 and time t > 0.