Reconsider Exercise 9.6.1 subject to the periodic boundary conditions that the eigenvalue splits. This means that if = 0, there is one eigenfunction for each eigenvalue, but as 0, two eigenvalues will approach each other (coalesce), yielding eigenvalues with two eigenfunctions. [Hint: It is necessary to consider a linear combination of both eigenfunctions ( = 0). For each eigenvalue, determine the specific combination of these eigenfunctions that is the unique eigenfunction when = 0.]

Limits and Discontinuity Notes Limits of sequences: 1/2 , k approaches ∞, and the fraction approaches 0. 0 is the limit as k approaches ∞. (2 -1)/2 , k approaches ∞, and the fraction approaches 1. 1 is the limit as k approaches ∞. Limits of average rates of change: finding final instantaneous velocity, calculate the rate of change over the last...