In LaTeX it is straightforward to include mathematical equations
and notation in your document. Often you will want to do this using
one of the maths environments, such as the `equation`

environment, i.e. you will
use `\begin{equation}...\end{equation}`

. Everything inside
this environment uses a "maths mode", which defines a large number of
useful commands and symbols.

Every `equation`

environment contains a single equation,
and this is usually numbered. You can use `\label{}`

to
reference it in your text just like any other object. If
you *don't* want your equation to be numbered then there's an
equivalent non-numbered environment
called `displaymath`

(NB *not* equation*).

If you want to write several equations together then you can use
the `eqnarray`

environment. At the end of each equation you
start a new line using `\\`

as
usual. The `eqnarray`

environment lets you align equations
so that, for example, all of the equals signs "=" line up. To do this,
put ampersand "&" signs around the text you want LaTeX to align, e.g.

```
\begin{eqnarray}
```

F &=& ma\\

V &=& IR

\end{eqnarray}

Each equation can be labelled separately, just put the label
command after the relevant equation. You can also suppress the
numbering for any particular equations by adding the
command `\nonumber`

after the equation; if you don't
want *any* of the equations to be numbered then use
the `eqnarray*`

environment instead.

Almost every conceivable symbol and operation is defined within LaTeX, and we only have time to go into a few here. Some of the most useful for scientists are:

`_{}`

the text in between the brackets is a subscript, e.g.`x_{i+1}=x_i + v_i t`

; if the subscript is only a single character you can omit the curly brackets.`^{}`

the text in between the brackets is a superscript, e.g.`E=mc^{2}`

; if the superscript is only a single character you can omit the curly brackets, e.g.`E=mc^2`

.`\lambda`

typesets the Greek letter lambda. Use`\Lambda`

for the capitalised form. The whole of the Greek alphabet is defined similarly.`\hat{}`

puts a "hat" on top of the text, for example you could use`\hat{H}`

for a Hamiltonian operator.`\frac{}{}`

is used to typeset a fraction. The numerator is the first argument, and the denominator the second.`\sum_{i=1}^{N}`

typesets a summation; the limits can be specified as subscripts and superscripts, as in this example. There's also`\prod`

for products, and`\int`

the integral sign; also`\oint`

for loop integrals. Limits are specified as subscripts and superscripts, as for summations.`\circ`

makes a small circle, most useful for doing things like`180^\circ`

to show 180-degrees.`\times`

makes a multiplication sign`\pm`

plus or minus (`\mp`

for minus or plus)`\surd`

the "square-root" sign`\equiv`

the "equivalent" sign`\approx`

the "approximately equal" sign`\sim`

the "of the order of" squiggly line`\neq`

the "not equal to" sign`\nabla`

the symbol for the vector differential operator "del"`\partial`

the partial derivative "curly d"`\forall`

the symbol for "for all"!`\exists`

the symbol for "there exists"!`\infty`

infinity`\imath`

special character for the imaginary number i (alternatively`\jmath`

if you use j for this number)`\hbar`

h-bar, i.e. Planck's constant over 2.pi`\ldots`

gives an ellipsis "..." (also`\cdots`

which puts the dots in the middle of the line,`\vdots`

which has three vertical dots and`\ddots`

which puts three dots diagonally from top-left to bottom-right)`\cdot`

makes a single dot`\Longrightarrow`

the "implies" arrow`\sin`

the sine function (also`\cos`

,`\tan`

,`\arcsin`

etc. as well as`\ln`

,`\log`

,`\exp`

and the hyperbolic functions)`\sqrt{x}`

is used for the "square-root" symbol. The mandatory argument is what is to be "rooted"; there's also an optional argument (put in square brackets before the curly ones) which defines the "power" of the root. E.g. the cube-root of two would be`\sqrt[3]{2}`

`\vert`

gives a small vertical line`x \atop y`

puts "x" above "y"

Sometimes you don't really want to put a full-blown equation in,
you just want to include a snippet in your text, or use some maths
"ideas" such as superscripts. To do this you can use the dollar sign
"$" - anything in between two dollar signs is typeset in maths mode, so
for example `the Hamiltonian $\hat{H}$ is the energy operator`

.

There are several different types of brackets in LaTeX, from the
ordinary round ones "(" and ")" to the curly "{" and "}" and the
square "[" and "]". Unfortunately the curly and square ones are used
by LaTeX to specify arguments, so if you want them to actually appear
in your equation you need to "escape" them, as it's called, by putting
a backslash in front of it, e.g. `\{`

. This method works
for any of the special symbols that LaTeX would normally treat as a
command, e.g. "%" or "$".

When you're typing equations it's common to find that the default
sizes for LaTeX's brackets are too small and they look a bit silly. To tell LaTeX to make brackets as big as a certain bit of an equation you use the `\left(`

and `\right)`

commands. The round bracket here can be replaced by any other bracket, or a full-stop which won't print anything but defines the start of the region. Try comparing

```
( \sum_{i=1}^N x_i p_i )
```

to

```
\left( \sum_{i=1}^N x_i p_i \right)
```

and you'll see what the `\left`

and `\right`

do!

Writing out matrices is a little bit tricky at first, which is why I've devoted a section to it! You need to use the `array`

environment inside the maths one. It's easiest to see with an example:

```
```

```
\left(
\begin{array}{ccc}
1 & 2 & 3\\
4 & 5 & 9\\
1 & -8 & 2
\end{array}
\right)
```

```
```

The argument to the array environment, `ccc`

, means
there are three centred columns (you don't need to specify the number
or rows). You can use `r`

or `l`

instead to
align any particular column "right" or "left" respectively.

Inside the `array`

environment the columns are separated
by "&", just as we used in the `eqnarray`

environment, and
new rows are made just using the new line command `\\`

.

The `array`

environment can take an optional argument to specify that the rows should be top-aligned, e.g. `\begin{array}{ccc}[t]`

, or use `[b]`

to ensure the rows are bottom-aligned.

Add some equations to your document, and reference them in the text. Add a superscript or some greek letters in some of your paragraphs.

- To typeset equations you can use the numbered environments
`equation`

for one equation, or`eqnarray`

for several, or the corresponding unnumbered environments`displaymath`

and`eqnarray*`

- You can put superscripts and other maths in text areas by putting dollar signs around them
`$`

- The
`\left`

and`\right`

commands can be used to ensure brackets are the correct size for the material in between them - The
`array`

environment can be used to typeset matrices

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