# 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?

• She is simply inconsistent. I would never you lower case $e$ for energy, especially in an expression where usual capital $E$ is already used for it. May 22 '15 at 13:53

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.

• “lower case e for anything rather than for elementary charge is wrong” – that's a bit of a strong statement, seeing as loads of people write $e^x = \exp(x)$. The lowercase e is also used for unit vectors, and I don't see anything bad about using it in other contexts as long as it's properly disambiguated. — In the context of the OP's question, the use $e$ seems indeed questionable though. May 22 '15 at 16:02
• @leftaroundabout, well, mathematical constants has to be printed in Roman (upright) type, so the base of natural logarithm has to be $\mathrm{e}$ and not $e$. The only issues is that it is difficult to do on a paper/board, but it is another story. Vectors has to be printed in bold or with an arrow on top (especially useful on a paper/board) so unit vectors has to be $\boldsymbol{e}_{i}$ or $\vec{e}_{i}$ but not $e_{i}$. May 22 '15 at 16:13
• In France we are free to use upper are lower, I saw $E$ or $e$ a lot of times and also $\Delta_r g$ sometimes... May 22 '15 at 16:25
• @Shadock, well, it's too bad of you, French. :D You'd better follow the International Standards. May 22 '15 at 16:54
• @Wildcat One may be advised, in certain style guides, to set mathematical constants in upright letters and so on but "have to" is clearly false. May 22 '15 at 18:27

The quantities and equations used with the International System of Units (SI) are called the International System of Quantities (ISQ). Many of the quantities as well as their recommended names and symbols are listed in the International Standard ISO/IEC 80000. They are considered almost universally accepted for use throughout the physical sciences.

According to this standard, the recommended symbol for the quantity ‘energy’ is an upper case $E$. (The quantity symbol is always written in italic type.)

Furthermore,

When, in a given context, different quantities have the same letter symbol or when, for one quantity, different applications or different values are of interest, a distinction can be made by use of subscripts.

This means, if you need more than one energy, you may for example write $E_1$ and $E_2$ or as in your example $E_\text{sys}$ and $E_\text{sur}$.

(Note that only subscripts that represent a physical quantity or mathematical variable are printed in italic type. All other subscripts are printed in roman type. Thus, writing $E_{sys}$ or $E_{sur}$ would be wrong.)

• +1 for mentioning the ISO Standard, though, I would not pay a lot attention to descriptive subscripts not being in Roman type since the equation was probably written by hands on a board. May 22 '15 at 16:18
• @Wildcat Sure but the typesetting advice still applies to the text of the question. May 22 '15 at 18:28
• I tend to just fix these when I see them - I've seen sinx before, some people just don't know how to put things in roman. May 22 '15 at 19:07