Also node that some partial fraction decomposition may be needed to find inverse transforms (as you would have seen in M274 or equivalent) Question 1: Consider a very long (semi-infinite) insulated conductive rod (shown in Figure 1). Initially this rod is at a constant ambient temperature: We will show later that this will result in an initial condition u(k0)-0. However, a controlled heating element is applied at the face corresponding to x 0, such that the face temperature (non-dimensional) increases linearly with time (t) ie.: ulot)- kt (wherek is a constant ) At this face of the rod, temperature ncreases linearly Figure 1 End of rod lof Length L) au u The heat equationc Part a) Using Laplace transform (together with Table 61 on page 224 of Kreyszig and extended table of transforms posted on web site) solve the non-dimensional heat equation according to the initial and boundary conditions Part b) Use Matlab (PRINT YOUR M FILE AND ATTACH) to plot the solution for a sequence of times from t-0 onwards to t 0.01 When t-0.01, at approximately what value of x is the semi infinite assumption no longer valid