1. [25 points) Solve problem 8.43 (Generalized Newton-Raphson method) from your textbook (Chapra and Canale, 7th Ed.) by writing a MATLAB code until the residual norm (IIRIl) is less that or equal to 10-12 Before you start writing your program, you must derive and write (as part of your hard copy submission) the following (a) Use the given expression for q, g2. gs, and that gl = 92-9s to first obtain a system of two nonlinear algebraic equations in Ti and T2 (say of the form f(T, T,)-0 and g(T,T,)s 0 ). (b) Write the expression for the Jacobian matrix (c) Determine a suitable starting solution for Ti and T. Your MATLAB code should have the following features as well: (i) After the iteration has converged, your program should print the final values of Ti and T2 on the command window, in C (ii) Display the number of iterations it took to converge (this excludes itera- tion), R for the final iteration in scientific notation, and approzimate relative percent errors of T, and T, (ean and ea, respectively), on the command window iii Plot anda as a function of the iteration number in a separate figure and EaT evaluated starting from in your MATLAB code. Remember that Ea the 1t iteration! (iv) Plot 11R, as a function of the iteration number in another figure. Here IIR the last exists starting with the 0 iteration (or initial or stating values) iteration (v) For both the error and norm plots, y-axis should be in log scale. Make sure the plot has markers at the data points, along with connecting lines (vi) Tabulate the following values as part of your hard copy submission: T1 ("O ,("O Iteration Number 0 f(T,.T) g(T,Z) ll an NA ra NA nth iteration 1. [25 points) Solve problem 8.43 (Generalized Newton-Raphson method) from your textbook (Chapra and Canale, 7th Ed.) by writing a MATLAB code until the residual norm (IIRIl) is less that or equal to 10-12 Before you start writing your program, you must derive and write (as part of your hard copy submission) the following (a) Use the given expression for q, g2. gs, and that gl = 92-9s to first obtain a system of two nonlinear algebraic equations in Ti and T2 (say of the form f(T, T,)-0 and g(T,T,)s 0 ). (b) Write the expression for the Jacobian matrix (c) Determine a suitable starting solution for Ti and T. Your MATLAB code should have the following features as well: (i) After the iteration has converged, your program should print the final values of Ti and T2 on the command window, in C (ii) Display the number of iterations it took to converge (this excludes itera- tion), R for the final iteration in scientific notation, and approzimate relative percent errors of T, and T, (ean and ea, respectively), on the command window iii Plot anda as a function of the iteration number in a separate figure and EaT evaluated starting from in your MATLAB code. Remember that Ea the 1t iteration! (iv) Plot 11R, as a function of the iteration number in another figure. Here IIR the last exists starting with the 0 iteration (or initial or stating values) iteration (v) For both the error and norm plots, y-axis should be in log scale. Make sure the plot has markers at the data points, along with connecting lines (vi) Tabulate the following values as part of your hard copy submission: T1 ("O ,("O Iteration Number 0 f(T,.T) g(T,Z) ll an NA ra NA nth iteration