in other words, it should be clear how the concentration profile is evolving as a function of time but the plot needs to be readable! Explain why your plot satisfies the boundary conditions and what happens at the steady state for the problem. 1.43 This problem involves analyzing the solution of subject to the initial condition T(x,0) = l and the boundary conditions T(0,t) = 0 and 7(1,) = 0. The Fourier series for the temperature is ! (a) Write a program that prints to the screen a formatted table of the values of the temperature at t = 0.1 for x = 0.1, 0.25, 0.5, 0.75, and 0.9 using 100 non-zero Fourier modes. Your program should use a subfunction that takes in the value of x, , and the number of Fourier modes and returns the value of the temperature at this point. You will use this subfunction in the rest of the problem. in other words, it should be clear how the concentration profile is evolving as a function of time but the plot needs to be readable! Explain why your plot satisfies the boundary conditions and what happens at the steady state for the problem. 1.43 This problem involves analyzing the solution of subject to the initial condition T(x,0) = l and the boundary conditions T(0,t) = 0 and 7(1,) = 0. The Fourier series for the temperature is ! (a) Write a program that prints to the screen a formatted table of the values of the temperature at t = 0.1 for x = 0.1, 0.25, 0.5, 0.75, and 0.9 using 100 non-zero Fourier modes. Your program should use a subfunction that takes in the value of x, , and the number of Fourier modes and returns the value of the temperature at this point. You will use this subfunction in the rest of the