What should you be able to do?

 
There are three aspects to the learning of physics:

1. The derivation, from previous first-principles ideas, of new relations and equations
2. The numerical use of these equations to calculate and predict how nature will act
3. The fusing of these understandings into concepts and intuition so that tedious calculation can be avoided when trying to determing the outcome of a system

The stereotypical physicist works only on 1 - derivations.
The stereotypical engineer works only on 2 - problem solving.

However, a deeper understanding, for both physicists and engineers, can be had with 3.  Unfortunately, this intuition usually is not attained until after lots of 2 - pattern recognition - and lots of 1 - mathematical sophistication.