Please Make A Note: Italics in Math Equations

Friday, July 9, 2010

Italics in Math Equations

I've seen plenty of papers in the literature with equations that are practically unreadable. My main issue is that these manuscripts fail to follow a very simple guide in mathematical notation:

If the term in question is a variable, then it should be italicized. All other terms should NOT be italicized.

Do NOT Italicize:

function names (sin, cos, log, ln etc...)
dimensionless numbers (Re, Pr, Ra...)
exact infinitesimal increments (dx, dy et... in BOTH integrals and differentials)
descriptive text

Here are some examples:

$\120dpi \begin{matrix} {\rm Incorrect} & {\rm Correct}\\[6pt] sin x & \sin x\\[6pt] log x& \log x\\[6pt] \dfrac{dx}{dt}&\dfrac{{\rm d}x}{{\rm d}t} \\[6pt] \dfrac{1}{Re}\nabla^2 \mathbf{u}&\dfrac{1}{\rm Re}\nabla^2 \mathbf{u}\\[6pt] \underbrace{\mathbf{u}\cdot\nabla \phi}_{convection \, term} & \underbrace{\mathbf{u}\cdot\nabla \phi}_{\rm convection \, term} \end{matrix}$

Another special case is with indices. The same rules still apply so that if the index is a variable, then it must be italicized. If it refers to a type of procedure (e.g. average, maximum...) it should NOT be italicized. If it refers to an entitye (e.g. gas, fluid, solid, particle...) then it should NOT be italicized. Some examples include

$\120dpi \begin{matrix} {\rm Incorrect} & {\rm Correct}\\[6pt] u_{avg} & u_{\rm avg}\\[6pt] T_{gas} & T_{\rm gas}\\[6pt] T_{g} & T_{\rm g}\\[6pt] Re_{d} & {\rm Re}_{\rm d} \end{matrix}$

In the last two examples, g and d refer to gas and particle diameter, respectively. Here, I am assuming that the particle diameter is a constant.

Voila!

Hope that helps a bit. If you think of something else, please feel free to add.

Cite as:
Saad, T. "Italics in Math Equations". Weblog entry from Please Make A Note. https://pleasemakeanote.blogspot.com/2010/07/italics-in-math-equations.html?m=0

3 comments:

SharafApril 14, 2011 at 3:38 PM
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SharafApril 14, 2011 at 3:55 PM
Useful, thanks.
It appears that in some style conventions two letter dimensionless group names (e.g. Re, Pr) are italic. This is the case, for example, in the Journal of Fluid Mechanics.
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timmay143July 9, 2011 at 11:37 PM
Ah, good post my friend. It can be quite confusing at times for some stuff. For example, should we italicize constants such C_1, etc. in, say, a general solution of an ODE? What about U_i,j for a difference equation? Should the i and j be italicized? I am guessing a and b should not be italicized for radii or L for Length, except in some of our conference papers on the BV and such they are. I'll try to think of some more. Thank you yNot.

Sharaf has a good point too. Some of the dimensionless abbreviations are italicized.
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Friday, July 9, 2010

Italics in Math Equations

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