# Correct line-breaking of long math expression

What is the correct way of breaking such unnumbered equation into multiple lines?

\begin{equation*}

\lim_{\bigtriangleup t \to 0^+}\int_{\bigtriangleup t}^{T} \! \int_{\Omega} \! D(t_1,x) \frac{\varphi(t_1-\bigtriangleup t,x)-\varphi(t_1,x)}{(-\bigtriangleup t)} \, \mathrm{d}x \, \mathrm{d}t_1

=\lim_{\bigtriangleup t \to 0^+} \int_{0}^{T} \! \int_{\Omega} \! D(t_1,x) \frac{\varphi(t_1-\bigtriangleup t,x)-\varphi(t_1,x)}{(-\bigtriangleup t)} \chi_{(\bigtriangleup t,T)}(t_1) \, \mathrm{d}x \, \mathrm{d}t_1

= \int_{0}^{T} \! \int_{\Omega} \! D(t_1,x) \frac{\partial \varphi}{\partial t_1} (t_1,x) \, \mathrm{d}x \, \mathrm{d}t_1 .

\end{equation*}

It's not an equation actually, I'm proving something in my thesis and I'm just modifying a math expression. So \multline is not this case I think. I used \split but then it can be aligned to the right side or the left side only because the expressions are too long and it would overfull.

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Welcome to TeX.sx! Have a look at mathmode with a lot of examples: ctan.org/pkg/voss-mathmode – Marco Daniel Apr 21 '13 at 13:02
@MarcoDaniel Thank you, this could be really helpful. – vessel Apr 21 '13 at 13:18

This is a tough formula to typeset; there is no "right way", such complex formulas often need specific treatment which depend on their size and also on subtle semantic issues.

Here is my proposal: the initial term is set on a line by itself and the two developments below it with aligned equals, indented to the right.

I changed \bigtriangleup into the customary \Delta; I also added a definition for the differential symbol that spares you from explicit \, commands. Finally I changed the definition of \phi to produce \varphi, so you can change them all to the "closed" variant by simply commenting the redefinition.

Why aligned inside equation*? Because this is a single block, so if you decide to number it, you can simply remove the *. With align* the result would be identical, but numbering it would require more steps.

\documentclass{article}
\usepackage{amsmath}
\newcommand{\diff}{\mathop{}\!\mathrm{d}}
\renewcommand{\phi}{\varphi}

\begin{document}
\begin{equation*}
\begin{aligned}
\lim_{\Delta t \to 0^+}
& \int_{\Delta t}^{T} \int_{\Omega}
D(t_1,x)
\frac{\phi(t_1-\Delta t,x)-\phi(t_1,x)}{(-\Delta t)}
\diff x \diff t_1
\\
&=\lim_{\Delta t \to 0^+}
\int_{0}^{T} \! \int_{\Omega}
D(t_1,x)
\frac{\phi(t_1-\Delta t,x)-\phi(t_1,x)}{(-\Delta t)}
\chi_{(\Delta t,T)}(t_1)
\diff x \diff t_1
\\
&=\int_{0}^{T} \! \int_{\Omega}
D(t_1,x)
\frac{\partial\phi}{\partial t_1}(t_1,x)
\diff x \diff t_1 .
\end{aligned}
\end{equation*}
\end{document}

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Oh, that's an exhaustive answer, thank you. I will use it. – vessel Apr 21 '13 at 13:22
+1 for paying such nice close attention to the semantics. If I could upvote twice I'd do it again for the time you spent. – Ethan Bolker Apr 21 '13 at 13:39

For example:

\documentclass{article}

\begin{document}
\begin{eqnarray*}
\lefteqn{
\lim_{\bigtriangleup t \to 0^+}\int_{\bigtriangleup t}^{T} \! \int_{\Omega} \! D(t_1,x) \frac{\varphi(t_1-\bigtriangleup t,x)-\varphi(t_1,x)}{(-\bigtriangleup t)} \, \mathrm{d}x \, \mathrm{d}t_1
}\\
&=&\lim_{\bigtriangleup t \to 0^+} \int_{0}^{T} \! \int_{\Omega} \! D(t_1,x) \frac{\varphi(t_1-\bigtriangleup t,x)-\varphi(t_1,x)}{(-\bigtriangleup t)} \chi_{(\bigtriangleup t,T)}(t_1) \, \mathrm{d}x \, \mathrm{d}t_1
\\
&= &\int_{0}^{T} \! \int_{\Omega} \! D(t_1,x) \frac{\partial \varphi}{\partial t_1} (t_1,x) \, \mathrm{d}x \, \mathrm{d}t_1 .
\end{eqnarray*}

But you'd rather write \Delta instead of \bigtriangleup.

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eqnarray! Run for your lives! – Jubobs Apr 21 '13 at 13:10
@Jubobs I do know eqnarray's limitations. But I also know, how to adjust this environment. – Przemysław Scherwentke Apr 21 '13 at 13:17
@PrzemysławScherwentke Thank you, this is looking well. Is there a rule of how to line-break equations and math expressions? For example would it be considered wrong if I separated each line by  and then it would be all centred? – vessel Apr 21 '13 at 13:17
@PrzemysławScherwentke Really, never ever use eqnarray. – egreg Apr 21 '13 at 13:20
@vessel Sugested eqnarray is the simplest one, making 3 columns. If you need more sophisticated breaking, please consider using of the amsmath package. – Przemysław Scherwentke Apr 21 '13 at 13:21