reference at the end of a bunch of equations

Question

\begin{equation}
\begin{aligned}
\frac{\partial f_j}{\partial x_j}(\textbf{y},t-\frac{\textbf{|x|}}{c_0} + \frac{\textbf{x} \cdot \textbf{y}}{c_0 |\textbf{x}|}) & = \frac{\partial f_j}{\partial t}(\textbf{y},t-\frac{\textbf{|x|}}{c_0} + \frac{\textbf{x} \cdot \textbf{y}}{c_0 |\textbf{x}|})\frac{\partial}{\partial x_j}(\textbf{y},t-\frac{\textbf{|x|}}{c_0} + \frac{\textbf{x} \cdot \textbf{y}}{c_0 |\textbf{x}|}) \\
               & = \frac{\partial f_j}{\partial t}(\textbf{y},t-\frac{\textbf{|x|}}{c_0} + \frac{\textbf{x} \cdot \textbf{y}}{c_0 |\textbf{x}|}) (-\frac{x_j}{c_0 |\textbf{x}|} + \frac{y_j}{c_0 |\textbf{x}|} - \frac{\textbf{x} \cdot \textbf{y}}{c_0|\textbf{x}|} )\\ 
               \label{3_7}
               & \approx -\frac{x_j}{c_0 |\textbf{x}|} \frac{\partial f_j}{\partial t} (\textbf{y},t-\frac{|x|}{c_0} + \frac{\textbf{x} \cdot \textbf{y}}{c_0 |\textbf{x}|}) , \ \ \ \  |\textbf{x}| \rightarrow \infty.  
               \end{aligned}
\end{equation}

I'd like the reference (3.7) to be located at the end of last equation. Could someone help? I have tried align instead of aligned but it doesn't work in amsmath

instead of equation plus aligned, use align and the (global, on amsmath) option tbtags. — barbara beeton, Jan 25 '18 at 16:38

Zarko · Answer 1 · 2018-01-25T16:04:32.823

simple use align and lines, where you not want equation numbers terminate with \notag or \nonumber:

instead \text{...} is more correct use \mathbf{...}. also the size of parentheses is adopted to expression within:

\begin{align}
\frac{\partial f_j}{\partial x_j}\left(\mathbf{y},t-\frac{\mathbf{|x|}}{c_0} + \frac{\mathbf{x} \cdot \mathbf{y}}{c_0 |\mathbf{x}|}\right)
    & = \frac{\partial f_j}{\partial t}(\mathbf{y},t-\frac{\mathbf{|x|}}{c_0} 
        + \frac{\mathbf{x} \cdot \mathbf{y}}{c_0 |\mathbf{x}|})\frac{\partial}{\partial x_j}(\mathbf{y},t-\frac{\mathbf{|x|}}{c_0} 
        + \frac{\mathbf{x} \cdot \mathbf{y}}{c_0 |\mathbf{x}|})
    \notag  \\
    & = \frac{\partial f_j}{\partial t}\left(\mathbf{y},t-\frac{\mathbf{|x|}}{c_0} 
        + \frac{\mathbf{x} \cdot \mathbf{y}}{c_0 |\mathbf{x}|}\right) 
        (-\frac{x_j}{c_0 |\mathbf{x}|}
        + \frac{y_j}{c_0 |\mathbf{x}|} - \frac{\mathbf{x} \cdot \mathbf{y}}{c_0|\mathbf{x}|})       
        \notag  \\
    & \approx -\frac{x_j}{c_0 |\mathbf{x}|} \frac{\partial f_j}{\partial t} \left(\mathbf{y},t-\frac{|x|}{c_0} 
        + \frac{\mathbf{x} \cdot \mathbf{y}}{c_0 |\mathbf{x}|}\right), 
          \qquad  |\mathbf{x}| \rightarrow \infty.
\end{align}

score 1 · Answer 2 · answered Jan 25 '18 at 18:23

You can use split together with the tbtags option to amsmath or aligned with the [b] option. The latter method doesn't need options to amsmath.

\documentclass[a4paper]{article}
\usepackage{geometry} % more generous line width
\usepackage[tbtags]{amsmath}

\newcommand{\vect}[1]{\mathbf{#1}}
\newcommand{\pder}[2]{\frac{\partial #1}{\partial #2}}

\begin{document}

\begin{equation}\label{3_7}
\begin{split}
\pder{f_j}{x_j}
  \Bigl(
  \vect{y},
  t-\frac{|\vect{x}|}{c_0} + 
  \frac{\vect{x} \cdot \vect{y}}{c_0 |\vect{x}|}
  \Bigr) 
& = \pder{f_j}{t}
    \Bigl(
    \vect{y},
    t-\frac{\vect{|x|}}{c_0} +
    \frac{\vect{x} \cdot \vect{y}}{c_0 |\vect{x}|}
    \Bigr)
    \pder{}{x_j}
    \Bigl(
    \vect{y},t-\frac{\vect{|x|}}{c_0} +
    \frac{\vect{x} \cdot \vect{y}}{c_0 |\vect{x}|}
    \Bigr)
\\
& = \pder{f_j}{t}
    \Bigl(
    \vect{y},t-\frac{\vect{|x|}}{c_0} +
    \frac{\vect{x} \cdot \vect{y}}{c_0 |\vect{x}|}
    \Bigr)
    \Bigl(
    -\frac{x_j}{c_0 |\vect{x}|} +
    \frac{y_j}{c_0 |\vect{x}|} - 
    \frac{\vect{x} \cdot \vect{y}}{c_0|\vect{x}|}
    \Bigl)\\
& \approx
    -\frac{x_j}{c_0 |\vect{x}|}\pder{f_j}{t}
    \Bigl(
    \vect{y},t-\frac{|x|}{c_0} +
    \frac{\vect{x} \cdot \vect{y}}{c_0 |\vect{x}|}),
    \qquad |\vect{x}| \rightarrow \infty.  
\end{split}
\end{equation}

\begin{equation}\label{3_7again}
\begin{aligned}[b]
\pder{f_j}{x_j}
  \Bigl(
  \vect{y},
  t-\frac{|\vect{x}|}{c_0} + 
  \frac{\vect{x} \cdot \vect{y}}{c_0 |\vect{x}|}
  \Bigr) 
& = \pder{f_j}{t}
    \Bigl(
    \vect{y},
    t-\frac{\vect{|x|}}{c_0} +
    \frac{\vect{x} \cdot \vect{y}}{c_0 |\vect{x}|}
    \Bigr)
    \pder{}{x_j}
    \Bigl(
    \vect{y},t-\frac{\vect{|x|}}{c_0} +
    \frac{\vect{x} \cdot \vect{y}}{c_0 |\vect{x}|}
    \Bigr)
\\
& = \pder{f_j}{t}
    \Bigl(
    \vect{y},t-\frac{\vect{|x|}}{c_0} +
    \frac{\vect{x} \cdot \vect{y}}{c_0 |\vect{x}|}
    \Bigr)
    \Bigl(
    -\frac{x_j}{c_0 |\vect{x}|} +
    \frac{y_j}{c_0 |\vect{x}|} - 
    \frac{\vect{x} \cdot \vect{y}}{c_0|\vect{x}|}
    \Bigl)\\
& \approx
    -\frac{x_j}{c_0 |\vect{x}|}\pder{f_j}{t}
    \Bigl(
    \vect{y},t-\frac{|x|}{c_0} +
    \frac{\vect{x} \cdot \vect{y}}{c_0 |\vect{x}|}),
    \qquad |\vect{x}| \rightarrow \infty.  
\end{aligned}
\end{equation}

\end{document}

Note that \textbf is wrong and it should be \mathbf, but I defined a more semantic macro. Consider also the \pder macro for the partial derivatives that eases input.

reference at the end of a bunch of equations

2 Answers2