The flux of heat in a metal bar of length l is given by the expression q(x) = −κ(x + 0.1)dt dx heat is removed from the bar along its length with a source term equal everywhere to f(x) = −x 2 the temperature at the left end is held at some reference temperature and the right end is insulated. (a) write a differential equation for the steady-state temperature profile in the bar with respect to the reference temperature, including boundary conditions (b) derive a finite difference approximation for the differential equation, and write the associated stencils honors students: treat the insulated boundary condition with a second-order method. (c) write a matlab function to solve the differential equation. write a script to run the model for several different cases. for all model runs use the length l = 0.5 and the reference temperature tref = 120. produce plots for all combinations of the number of grid intervals n and the coefficient κ: n = {8, 16, 32} and κ = {0.01, 0.005, 0.001}. plot the results for each κ on a single plot: in total there will be three plots with three curves each