Equation (1.1) represents a one-dimensional, steady state, heat conduction with heat generation. d²T dx² --807 cos(x)=0, 7(0)=0, T'(0.5)=30 (1.1) a) Express the physical meaning of the boundary conditions in words. By using U and V to replace T, rewrite Equation (1.1) to become two ODEs of the first order. The initial conditions of these two ODEs must also be stated clearly. One of the initial conditions can be obtained from Equation (1.1), while another initial condition can be assumed to take the value of 5. Use the fourth order Runge-Kutta method to find U and V at x = 0.25m. Take 0.25 as the step size. b) The shooting method is used to find V at x = 0.5m. By using U and V to replace T, rewrite Equation (1.1) to become two ODES of the first order. One of the initial conditions can be obtained from Equation (1.1) and another can be assumed to take value of 5. Use the explicit Euler method with the step size of 0.25 to solve Equation (1.1). It is impossible to obtain T'(0.5) = 30 that matches with exact value in Equation (1.1). Thus, doing further calculations, explain the next steps so that T'(0.5)= 30 is obtained. Based on the problem statement given in part b), students are required to use MS Excel to investigate the exact value of Ka. Plot V (0.5)-30 versus Ka and identify the exact value of Ka in the graph. Repeat the calculation in part b) using the exact value of Ka and prove that T'(0.5)= 30.