1. For the 1-D bar system, assume k = 30 W/m−◦C, L = 0.4 m, α = 50◦C, β = 20◦C,

1. For the 1-D bar system, assume k = 30 W/m−◦C, L = 0.4 m, α = 50◦C, β = 20◦C,
and q(x) = 4000x(L − x) W/m3. For N = 4, write down the three equations in the
system Au = f and solve for the vector u. No coding necessary for this part. Plot
the temperature solution along the bar using the temperatures at the five nodes. Use
Python for plotting purposes.
2. Consider the following data:
xi 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
ui 22.5 26.4 28.4 32.5 37.4 40.2 32.0 29.0 25.2
(a) Calculate the first-order accurate finite difference approximations to the first derivative
u′(x) at all xi.
(b) Next, calculate the corresponding second-order accurate finite difference approximations.
(c) Compare the two sets of approximations by plotting the approximations against x.
Again, use Python for this purpose.