LaTeX example
Using TeX allows you to create professional-quality documents with mathematical symbols without too much trouble. When you want to use text,
simply type. Starting a new line will give you a new paragraph, which is
automatically indented. If you don’t want it indented, precede that line with
noindent with a backslash in front of it. Where TeX really shines though is in
math mode. If you want to use math mode inside a paragraph, use the $ to
enter math mode and use $ again to P
exit. For example, the two-dimensional
(linear) transport equation is ut = 2i=1 ai uxi , where the ai are constants.
Often, you will want to use math symbols on lines by themselves; do this with
the square brackets [ and ]. For instance the general form of a quasilinear
second-order homogeneous PDE in n variables x1 , x2 , . . ., xn is given by
n
X
∂2u
aij (x, u, Du)
Qu =
+ b(x, u, Du) = 0
∂xixj
i,j=1
where the aij and b are given functions and Du is the gradient of the unknown
function u.
You can also label equations so that it is easy to refer to them later. The
heat equation is
∂u
= κ∆u.
(1)
∂t
A solution u to equation (1) describes the distribution of temperature in a
uniform solid. The constant κ depends on physical properties of the solid.
You can also use tex to construct arrays or tables. For example, the
Cauchy problem for the wave equation is:

utt = ∆u in D

u = f on ∂D

∇u · ~n = g on ∂D
Here D is some domain, f and g are given functions, ∇u is the gradient of
u, and ~n is the outward unit normal to ∂D. In this example the rcl in braces
appearing after the begin command sets up an array with three columns, the
first right-justified, the second centered and the third left-justified. The & is
used to denote the end of one column and the beginning of the next. When
you reach the end of a row in the array (other than the last one), type two
backslashes. This will begin a new row.
1