A regular singular point was defined. This type of singular point usually necessitates that we introduce an extra boundary condition, namely that the solution is bounded. This was illustrated using an example of radial heat flow.
Another type of singularity arises with semi-infinite and infinite intervals, again necessitating a boundedness boundary condition. This was illustrated with an infinitely long cooling fin.
Next, the method of Green's Functions was presented. (Section 0.5 of the textbook.) When one homogeneous solution is chosen to satisfy the left boundary condition, and the other homogeneous solution is chosen to satisfy the right boundary condition, then the Green's function takes on a particularly simple form, involving the Wronskian.
The Green's function method was illustrated with a simple example (which can be solved by inspection, but this makes it easy to check that the method gives the correct answer).