Align (environment)

The align environment is used for two or more equations when vertical alignment is desired; usually binary relations such as equal signs are aligned.

American Mathematical Society, User's Guide for the amsmath Package

Introduction to align

For all intents and purposes, the align environment is a replacement for the eqnarray environment and all its warts. Rather than

\begin{eqnarray*}
x^2 + y^2 &=& 1
\\ y &=& \sqrt{1 - x^2},
\end{eqnarray*}

one can type

\begin{align*}
x^2 + y^2 &= 1 \\
y &= \sqrt{1 - x^2}.
\end{align*}

Benefits over eqnarray

Besides the slightly simpler syntax, you side-step bugs documented by Lars Madsen for The PracTeX Journal:

• Inconsistent spacing around binary symbols like

= and +;

• Overwriting equation numbers; and
• Silent label mismatch.

Multiple equations on one line

Besides being used for aligning binary symbols, the ampersand can also mark an invisible alignment for separating columns of equations. For example,

\begin{align}
    u  &= \arctan x             &  dv &= 1 \, dx  \\ 
    du &= \frac{1}{1 + x^2} dx  &  v  &= x.
\end{align}

produces:

${\begin{aligned}u&=\arctan x&dv&=1\,dx\\du&={\frac {1}{1+x^{2}}}dx&v&=x.\end{aligned}}$

Preamble

To use align, import the amsmath package in your preamble.

.....
\usepackage{amsmath}
.....

\begin{document}
\begin{align*}
    u  &= \arctan x             &  dv &= 1 \, dx  \\ 
    du &= \frac{1}{1 + x^2} dx  &  v  &= x.
\end{align*}
\end{document}