Either you misunderstood what the teachers said, or the teachers didn't explain this the right way.
With few exceptions, there are no 'purely DC' circuits, not even (perhaps especially!) power supplies.
Inductors and caps enjoy a lot of use because of their transient features. The examples that follow are pretty simplistic, and hardly scratch the surface of where and why these components get used.
As an example, let's look at the stuff running from the DC power supply. All those circuits (if they are doing anything remotely interesting) are generating switching noise that couples back into the supply (and disturb their own local version of the supply). Caps are used for two main purposes in this area
- Transient suppression. Get rid of those nasty transients generated by the chips themselves.
- Bulk bypass. In this application, we're using the cap as a small 'battery' to provide curent to the device when the main power supply droops (perhaps the load is too high - that certainly happens in some designs).
The vast majority of such caps are used in the transient response area. This ignores the bulk caps and loop filters on a switchmode supply (but that's a subject for another day).
Inductors, likewise, have characteristics we can use. As another example, when I have designed very high speed interconnects (2.5 -
10Gb/s), the drivers are universally 'CML'. This is current mode logic, which means the driver 'consumes' a (fairly) constant current regardless of the output state. To prevent the high speed switching from interfering with this (desired) constant current, I put small inductors in series from the power supply to these chips. (An inductor tends to oppose changes in current).
Of course, switch mode supplies require an inductor for other reasons.
As I said, the uses for caps and inductors are wide and varied, and this barely starts the conversation.
Hope that helps clue level increase.