Why does my professor use both the upper, and the lower, case literal of a letter to symbolize the same concept? In one of our slides, the professor has written 


  $ \Delta E_{sys} = -\Delta e_{sur}$


Where $E_{sys}$ symbolizes the energy of a given system, and $e_{sur}$ symbolizes the energy of the surroundings of that system. 

On a few occasions, she's used both the upper, and the lower, case literal of a single letter as symbols of a single concept. 

Is there a notational convention that requires the use of an upper case literal of a letter in some circumstances and the use of its counterpart in other circumstances?
Of course, there is a convention. In physics $E$ usually stands for energy, $e$ for elementary charge. You professor is inconsistent, to say the least. In my opinion using lower case $e$ for anything rather than for elementary charge is wrong by itself, and using it for energy is simply ridiculous. Besides, I don't see any reason for doing so.

P.S. During my university years I had a professor who randomly picked letters for physical quantities every lecture. :D Today I think of it with a smile, but at that time I hated both his lectures and him personally.