Appendix A
Global list of symbols and units
“What’s the good of Mercator’s North Poles and Equators
Tropics, Zones, and Meridian Lines?”
So the Bellman would cry: and the crew would reply
“They are merely conventional signs!”- Lewis Carroll,The Hunting of the Snark
Notation is a perennial problem for scientists. We can give each quantity whatever symbolic name
wechoose, but chaos would ensue if every writer chose completely different names for familiar
quantities. On the other hand, using standard names unavoidably leads to the problem of too
many different quantities all having the same name. The notation listed below tries to walk a
line between these extremes; when the same symbol has been pressed into service for two different
quantities, the aim has been to ensure that they aresodifferent that context will make it clear
which is meant in any given formula.
Mathematical notation
Vectors are denoted by boldface:v=(vx,vy,vz). The symbolv^2 refers to the total length-squared
ofv,or(vx)^2 +(vy)^2 +(vz)^2 .Vectors of length equal to one are flagged with a circumflex, for
example, the three unit vectorsxˆ,ˆy,ˆzor the tangent vectorˆt(s)toacurve at positions. The
symbol d^3 ris not a vector, but rather a volume element of integration.
Often the dimensionless form of a quantity will be given the same name as that quantity, but
with a bar on top.
The symbol “≡”isaspecial kind of equals sign, which indicates that this equality serves as a
definitionof one of the symbols it contains. The symbol “=” signals a provisional formula, or guess.?
The symbol “∼”means “has the same dimensions as.” The symbol “∝”means “is proportional
to.”
The symbol|x|refers to the absolute value of a quantity; if the quantity is a vector,|v|is
interpreted as the length of that vector. The notation〈f〉refers to the average value of some
functionf,with respect to some probability distribution.
The symbol ddES
∣∣
N refers to the derivative ofSwith respect toEholdingNfixed. But the
symbolddβ
∣∣
∣β=1F,orequivalentlyddFβ∣∣
∣β=1refers to the derivative ofFwith respect toβ,evaluated
at the pointβ=1.
©c2000 Philip C. Nelson