Mathematical Symbols and Special Characters
COMSOL Multiphysics supports a subset of the LaTeX language for creating equations as part of the documentation or in user-developed physics interfaces and other applications. Commands include Greek and other characters, mathematical symbols and operators, arrows, text and font formats, and environments for text and mathematical typesetting. The following tables and lists contain the commands that are available for creating equations and other mathematical text.
Greek and Other Characters
The following table contains the supported lowercase and uppercase Greek letters and the Swedish character Å in math mode:
α
β
Γ
γ
Δ
δ
ζ
η
Θ
θ
ι
κ
Λ
λ
μ
ν
Ξ
ξ
Π
π
ρ
Σ
σ
τ
Υ
υ
Φ
ϕ
φ
χ
Ψ
ψ
Ω
ω
The following tables contain the supported lowercase and uppercase Greek letters and other characters in text mode (so that no math mode enclosures using $ are needed):
Α
α
Β
β
γ
δ
Ε
ε
Ζ
ζ
Η
η
Θ
θ
Ι
ι
Κ
κ
Λ
λ
Μ
μ
Ν
ν
ξ
Ο
ο
π
Ρ
ρ
Σ
σ
Τ
τ
Υ
υ
Φ
φ
ϕ
Χ
χ
Ψ
ψ
Ω
ω
÷
¬
×
Ω
The symbols in the tables above use the text font if the symbol exists; otherwise, they use the corresponding math font.
Accents
The following accents are available:
Table 21-8: Accents.
Mathematical Symbols and Operators
The following mathematical symbols and operators are available:
The following table lists the available “big” mathematical operator as well as binary mathematical operators and relations:
±
×
Arrows
The following table includes the available types of arrows:
Table 21-11: Arrows.
Delimiters and Environments
The following tables includes the available delimiter, spaces, and environments, including Unicode characters:
End the array environment (see Note below)
Invoke the array environment (see Note below)
The \left and \right commands must be used in pairs to provide flexible delimiters that fit the formula inside. Put the desired delimiter — ( and ), for example — immediately after the \left and \right commands. For example, \left( \frac{x}{y} \right) provides x/y as a fraction within parentheses that fit the expression’s size.
The \makebox command creates a box for the text. In addition to the \makebox{text} syntax, you can also use \makebox[width]{text}, where the width can be \depth, \height, \width, and \totalheight (which is the box’s height plus its depth), or a multiple of those widths. You can also use a width with a unit such as 10em for 10 “M” widths or 20mm for 20 mm width. The \makebox[width][position]{text} syntax provides an optional position of the text within the box: c for centered text (the default), l for flush left, or r for flush right.
The \begin and \end commands must be used in pairs to mark the beginning and end of an environment. The only supported environment is the array. For example, \begin{array}{clcr} 1 & 2 & 3 \\ 4 & 5 & 6\end{array} creates a matrix with 2 rows and three columns.
Mathematical Function Names
The following function commands provide the function name using a Roman font:
Table 21-13: Functions.
Special Mathematical Typesetting
There are two mathematical formula components with a special syntax: \frac for fractions and \sqrt for roots:
Use the syntax \frac{numerator}{denominator} to create a fraction. For example, the expression \frac{n!}{k!(n-k)!} produces the following output:
Use the syntax \sqrt[order]{expression} to create a root surrounding an expression. The [order] argument is optional; without it, the syntax produces a square root. For example, \sqrt[n]{1+x^2} produces the following output:
Text and Font Elements
The following syntax elements are available for creating different text elements and fonts:
The \textsuperscript and ^ syntax alternatives are identical for creating superscripts. Likewise, \textsubscript and _ are identical for creating subscripts.
Special Control Sequences and Characters
The following special control sequences and special characters are available:
\<space>