Thursday, March 30, 2017

orthogonality of eigenfunctions

reality of eigenvalues

uniqueness of eigenfunctions

Derivation

Conditions guaranteeing positivity of eigenvalues

Minimization principle: statement, utility, proof

Correction: the class of functions we're minimizing over can be extended to functions that are continuous on [a,b], have a piecewise continuous derivative on (a,b), and satisfy the BCs.

Next: Examples and proof of minimization principle