Greek symbols are very important in equations: \phi, \pi, \Xi. eLyXer offers a complete set in both upper case: \Gamma\ldots\Omega and lower case: \alpha\ldots\omega. Also the AMS italicized upper case: \varGamma\ldots\varOmega.
eLyXer supports the whole set of math symbols in John D. Cook's list: \exists\partial\nabla\geq. It can also render a few more: \propto\times. You also get all symbols from Markus Kuhn's list: \bigodot\amalg.
There are other symbols like arrows: \leftarrow\rightarrow, or geometrical shapes: \circ, \square. eLyXer offers limited support for them. You might also want to use financial symbols in formulae: \yen\euro\$.
Equations look good when items are properly separated. The main separation is the Medium Mathematical Space: x=3.
Note: if you are viewing the non-Unicode version math.html of this page then you are in fact seeing midspaces, which are very similar but not exactly the same: \frac{4}{18}\mathrm{em} for medium mathematical spaces versus \frac{1}{2}\mathrm{en}, where 1\mathrm{em}=2\mathrm{en}. Try out the Unicode version math-unicode.html — and viceversa. You can check out what version this page is in the page title.
The command \raisebox is useful to, surprisingly, raise a little box,
By default, letters denote variables and are taken from the \mathnormal font, which is italic, \alpha x+\alpha y=\alpha(x+y), with the exception of upright capital Greek letters, G\ne\Gamma.
Function names should be upright: \sin(2\pi),\log(x),\tan\delta.
Mathematical fonts used in equations include \mathrm{Roman} (\mathrm), \mathsf{Sans\: Serif} (\mathsf), \mathtt{Typewriter} (\mathtt), \mathbf{Bold} (\mathbf), \mathscr{SCRIPT} (\mathscr), \mathcal{CALLIGRAPHIC} (\mathcal), \mathbb{BLACKBOARD\: BOLD} (\mathbb), and \mathfrak{Fraktur} (\mathfrak). For the latter, some single characters are translated to their Unicode equivalents: \mathscr{F}, \mathbb{F}, \mathfrak{F}.
Regular text in a formula can be achieved via text font commands like \textrm: 5\:\textrm{to}\:10, via boxes like \mbox (prevents line breaks): 6\mbox{ is more than }5, or the AMSmath \text macro (scales like math symbols) \text{base}_{\text{sub}}^{\text{super}}. The content of an mbox is processed in LaTeX text mode. This allows text font commands, e.g. a switch to sans-serif-bold-italic, or the phonetic alphabet: \mbox{\textbf{\textsf{\textbf{\textit{sfbfit}}}}, \textipa{tipa}}.
Units should be written upright, either with \mathrm or with macros from the units package, e.g. as simple unit, \unit{km}, with magnitude, \unit[57]{km}, with fractional unit, \unitfrac[200]{km}{h}, or with a fraction before the units, \unit[\nicefrac{3}{2}]{km}, \unit[\frac{7}{16}]{s}.
\lim_{x\rightarrow\infty}f(x) should appear as x\rightarrow\infty in italics, and «lim» in plain style. In display mode, a limit must appear below the main symbol:
where the sum’s limits should appear below (i=1) and above (\infty) the \sum. The placement of the integral limits depends on the document class: LaTeX standard classes place them right to the \int. Limits are shown to the right in inline formulae: \sum_{i=1}^{\infty}x and \intop_{i=1}^{\infty}x.
The placing of limits can be configured with the \limits and \nolimits macros:
An inline array \left[\begin{array}{cc}
a & b\\
c & d\end{array}\right] is always shown in the same line. In display mode, the array is shown on its own line:
Arrays are separated by variable-size brackets: \left(\begin{array}{cc}
a & b\\
c & d\end{array}\right)\left[\begin{array}{cc}
a & b\\
c & d\end{array}\right]\left\{ \begin{array}{cc}
a & b\\
c & d\end{array}\right\} \left\langle \begin{array}{cc}
a & b\\
c & d\end{array}\right\rangle \left|\begin{array}{cc}
a & b\\
c & d\end{array}\right|which might also differ on right and left \left(\begin{array}{cc}
a & b\\
c & d\end{array}\right) or use the empty opening \left\{ \begin{array}{cc}
a & b\\
c & d\end{array}\right. or closing: \left.\begin{array}{cc}
a & b\\
c & d\end{array}\right|. There are also fixed-size big brackets, e.g. \bigl\langle f\bigr\rangle.
Now it’s time for user-defined commands (sometimes called “macros”).
Definitions can be added as macros
\newcommand{\stupidroot}[2]{\sqrt[#1]{#2}}
{\sqrt[#1]{#2}}
. Then they can be used in formulae: \stupidroot 12. They can accept default parameters
\newcommand{\defaultroot}[2][4][5]{\sqrt[#1]{#2}}
{#1\sqrt{#2}}
. Again, useful in formulae: \defaultroot.
Other definitions from the preamble can be used: \preambleroot{3}{4}.
Definitions on the fly are also possible: \newcommand{\ontheflyroot}[2]{\sqrt[#1]{#2}}\ontheflyroot{7}{8}, and used with different values: \ontheflyroot{a}{b}.