The above (top) design is one for a adjustable regulated voltage using an IC. The bottom schematic is the actual design of the IC regulator. My question is, am I missing an obvious way to derive the relationship for Vo? How does this design work, anyway? I figured it had something to do with the feedback to the ICs reference voltage (ground, middle pin). If it were me, I would just use a fixed voltage regulator, like the 7805, ground the middle pin and take the output between R1 and R2 (with R2 being shunted by a cap). In this way, the output is simply a voltage divider. Although, perhaps I am just not seeing the merit of using a true adjustable IC like this one.