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.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 *λ*_{3} 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.

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

5.6.1a (Estimation of eigenvalue with Rayleigh Quotient.)