This is a case where visual formatting seems necessary, so it should be dealt with only in the very last stage of document preparation.
You can pretend that the very last part of the formula “is not there”:
\documentclass[12pt, oneside]{scrbook}
\usepackage{amsmath,mathtools}
\DeclareMathOperator{\E}{E}
\newcommand{\with}{\,;}
\newcommand{\dx}{\mathop{}\!\mathrm{d}}
\newcommand{\expect}[2][]{\E\if\relax\detokenize{#1}\relax\else_{#1}\fi \left[#2\right]}
\begin{document}
\begin{equation}
\begin{aligned}
\mu_{D_-}
&= \expect{f'(S_-) \cdot \sum_{i=1}^{N} W D} \\
&= N \mu_W \mu_D \int_{-\infty}^{\infty} f'(s) p_\mathcal{N}(s \with \mu_{S_-}, \sigma_{S_-}) \dx{s} \\
\sigma_{D_-}^2
&= \expect{f'(S_-)^2 \cdot \left(\sum_{i=1}^{N} W D\right)^2} - \mu_{D_-}^2 \\
&= N(\sigma_W^2 \sigma_D^2 + \mu_W^2 \sigma_D^2 + \sigma_W^2 \mu_D^2 + N \mu_W^2 \mu_D^2)
\int_{-\infty}^{\infty} f'(s)^2 p_\mathcal{N}(s \with \mu_{S_-}, \sigma_{S_-}) \dx{s}
\mathrlap{{} - \mu_{D_-}^2 \,.}
\end{aligned}
\end{equation}
\end{document}
I amended your definition of \dx
, because it would give wrong spacing on the right. Also \;
seems too big for \with
(to be honest, I wouldn't add a space before the semicolon).
Your definition of \expect
with automatic \left
and \right
produces too big delimiters in many cases (see the third line, for instance).
Here's an amended version that uses xparse
and mathtools
features; the syntax for \expect
is
\expect{formula}
\expect[\big]{formula}
\expect*{formula}
\expect_{sub}{formula}
\expect_{sub}[\big]{formula}
\expect_{sub}*{formula}
as shown in the added equation. In the optional argument one can use \big
, \Big
, \bigg
or \Bigg
; the *-version uses \left
and \right
.
Note also the addition of \,
and \!
in a few places.
I suggest to use the fleqn
environment from nccmath
, which works somewhat like subequations
, and the alignat*
environment, which gives you full control on the spacing between the alignment columns:
\documentclass{article}
\usepackage{amsmath, nccmath}
\usepackage{xcolor}
\usepackage[showframe]{geometry}
\begin{document}
\mbox{}\bigskip
\begin{fleqn}
\begin{alignat*}{2}
\color{red}f:x^2+y^2 & =4, & \qquad\color{blue}f(3) & =2\\
\color{red}g:x^2-y^2 & =2, & \color{blue}g(4) & =1
\end{alignat*}
\end{fleqn}
\end{document}
Best Answer
I suggest you place rows 2 and 3 inside nested
aligned
environments.The following screenshot shows the outputs of both your original code and the suggested replacement code.
Speaking for myself, I can't help but wonder what you could possibly be trying to achieve by centering the second equation number across rows 2 and 3 of the 3-row construct. That said, I also can't fathom why you're using an
flalign
environment instead of analign
environment.