Please answer the attached question for the graphs in part A and graphs in part B. The 3 questions must be done for both parts, please solve them for both and show work. Thank you!

1. [14 points] Heat equation on a bounded domain Suppose you are measuring the temperature along a thin bar of length 5 meters (m). The bar is made of iron, which has thermal conductivity k = 59 W/(m . K) (watts per meter kelvin). Heat flow inside the bar is governed by the one-dimensional heat equation: aT 2- T Ot D 0