5.3

5.3.3 (Gerneral 2nd order ODE to Sturm-Liouville form.)

5.3.5 (Verifying that SL properties are true for a particular BVP where we know all the eigenstuff.)

5.4

5.4.X Use this code along with trial-and-error to find the third smallest eigenvalue of the non-uniform bar heat flow problem we have considered in class. Also make a plot of the corresponding eigenfunction. Determine λ₃ accurately enough that |φ^′(20)| (which should be exactly 0) is no bigger than .001.

First pass:

lambdamin = .18
lambdamax = .19
nlambda = 21

Results:
lambda = 0.189               : phi'(L) = 0.01822411398646856
lambda = 0.1895              : phi'(L) = -0.002103058608923347

Second pass:

lambdamin = .189
lambdamax = .1895
nlambda = 21

Results:
lambda = 0.189425            : phi'(L) = 0.0009408342562378103
lambda = 0.18945             : phi'(L) = -7.400160917431231e-05

At 0.18945, |phi'(20)| is much smaller than the specified maximum of 0.001.

5.5

5.5.1c (Show a SL problem is "self-adjoint".)

5.6

5.6.1a (Estimation of eigenvalue with Rayleigh Quotient.)