(latex2e.info)Math formulas

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16 Math formulas
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Produce mathematical text by putting LaTeX into math mode or display
math mode (Note: Modes).  This example shows both.

     The wave equation for \( u \) is
     \begin{displaymath}
       \frac{\partial^2u}{\partial t^2} = c^2\nabla^2u
     \end{displaymath}
     where \( \nabla^2 \) is the spatial Laplacian and \( c \) is constant.

Math mode is for inline mathematics.  In the above example it is invoked
by the starting '\(' and finished by the matching ending '\)'.  Display
math mode is for displayed equations and here is invoked by the
'displaymath' environment.  Note that any mathematical text whatever,
including mathematical text consisting of just one character, is handled
in math mode.

   When in math mode or display math mode, LaTeX handles many aspects of
your input text differently than in other text modes.  For example,

     contrast x+y with \( x+y \)

in math mode the letters are in italics and the spacing around the plus
sign is different.

   There are three ways to make inline formulas, to put LaTeX in math
mode.

     \( MATHEMATICAL MATERIAL \)
     $ MATHEMATICAL MATERIAL $
     \begin{math} MATHEMATICAL MATERIAL \end{math}

The first form is preferred and the second is quite common, but the
third form is rarely used.  You can sometimes use one and sometimes
another, as in '\(x\) and $y$'.  You can use these in paragraph mode or
in LR mode (Note: Modes).

   To make displayed formulas, put LaTeX into display math mode with
either:

     \begin{displaymath}
       MATHEMATICAL MATERIAL
     \end{displaymath}

or

     \begin{equation}
       MATHEMATICAL MATERIAL
     \end{equation}

(Note: displaymath, Note: equation).  The only difference is that
with the 'equation' environment, LaTeX puts a formula number alongside
the formula.  The construct '\[ MATH \]' is equivalent to
'\begin{displaymath} MATH \end{displaymath}'.  These environments can
only be used in paragraph mode (Note: Modes).

   The two mathematics modes are similar, but there are some
differences.  One involves the placement of subscripts and superscripts;
in display math mode they are further apart and in inline math mode they
are closer together.

   Sometimes you want the display math typographical treatment to happen
in the inline math mode.  For this, the '\displaystyle' declaration
forces the size and style of the formula to be that of 'displaymath'.
Thus '\(\displaystyle \sum_{n=0}^\infty x_n\)' will have the limits
above and below the summation sign, not next to it.  Another example is
that

     \begin{tabular}{r|cc}
       \textsc{Name}  &\textsc{Series}  &\textsc{Sum}  \\  \hline
       Arithmetic     &\( a+(a+b)+(a+2b)+\cdots+(a+(n-1)b) \)
                        &\( na+(n-1)n\cdot\frac{b}{2}\)  \\
       Geometric      &\( a+ab+ab^2+\cdots+ab^{n-1} \)
                        &\(\displaystyle a\cdot\frac{1-b^n}{1-b}\)  \\
     \end{tabular}

because it has no '\displaystyle', the 'Arithmetic' line's fraction will
be scrunched.  But, because of its '\displaystyle', the 'Geometric'
line's fraction will be easy to read, with characters the same size as
in the rest of the line.

   The American Mathematical Society has made freely available a set of
packages that greatly expand your options for writing mathematics,
'amsmath' and 'amssymb' (also be aware of the 'mathtools' package that
is an extension to, and loads, 'amsmath').  New documents that will have
mathematical text should use these packages.  Descriptions of these
packages is outside the scope of this document; see their documentation
on CTAN.

Subscripts & superscripts

Also known as exponent or index.

Math symbols

Various mathematical squiggles.

Math functions

Math function names like sin and exp.

Math accents

Accents in math.

Over- and Underlining

Things over or under formulas.

Spacing in math mode

Thick, medium, thin, and negative spaces.

Math miscellany

Stuff that doesn't fit anywhere else.