equation exceeds page width after changing document class from "article" to "beamer"

Question

I write article at first, but I also need pdf in beamer version. But I found for those long equations appears fine in "article" will exceed the page width in "beamer" mode. So is there a method to avoid this automatically?

A MWE is as follows:

\documentclass[12pt]{beamer} \usepackage{amsmath,amssymb,amsthm}

\begin{document}
  \begin{equation}\label{}
    \int_C {{\mathbf{F}}\left( {x,y} \right) \cdot d{\mathbf{r}}}  = \int_C {\left( {f\left( x \right){\mathbf{i}} + g\left( y \right){\mathbf{j}}} \right) \cdot \left( {dx{\mathbf{i}} + dy{\mathbf{j}}} \right)}  = \int_C {f\left( x \right)dx}  + \int_C {g\left( y \right)dy}
  \end{equation}
\end{document} 

gives

After change documentclass from article to beamer

\documentclass[12pt]{beamer}
\usepackage{amsmath,amssymb,amsthm}

\begin{document}
  \begin{equation}\label{}
    \int_C {{\mathbf{F}}\left( {x,y} \right) \cdot d{\mathbf{r}}}  = \int_C {\left( {f\left( x \right){\mathbf{i}} + g\left( y \right){\mathbf{j}}} \right) \cdot \left( {dx{\mathbf{i}} + dy{\mathbf{j}}} \right)}  = \int_C {f\left( x \right)dx}  + \int_C {g\left( y \right)dy}
  \end{equation}
\end{document} 

gives

Answer 1

I suggest you do the following:

• Insert a line-break instruction (\\) and one additional alignment point indicator (&). That way, TeX can tell where to break the lines and on which points to align the rows.

With this change in place, one gets:

I would like to urge you to consider making a few more changes:

• Use a \notag instruction at the end of the first row to suppress the equation number on that line.

• Delete all \left and \right directives. Doing so will markedly improve the spacing around the parentheses. Plus, they don't "do" anything anyway, in terms of changing the size of the parentheses: the material they enclose isn't tall or deep, and thus the size of the parentheses remains at the smallest possible value. If you really need to change the sizes of the parentheses, use \bigl( and \bigr), as is done in one case in the code below.

• Get rid of all curly braces, with the exception of those associated with the \mathbf directives. In TeX's math mode, having all these curly braces running around is not innocuous: Surrounding some material with curly braces converts its type to "math-ordinary", obliterating any chance TeX may have to fine-tune the spacing around items of type "math-open", "math-close", etc.

• Replace the \cdot directives with \, (thinspace), and insert \, before the "differential operators" -- d\mathbf{r}, dx, and dj.

\documentclass[12pt]{beamer}
\usepackage{amsmath,amssymb,amsthm}
\begin{document}

\begin{frame}
  \begin{align}
    \int_C \mathbf{F}( x,y ) \, d\mathbf{r}  
    &= \int_C \bigl( f( x )\,\mathbf{i} + g( y )\,\mathbf{j} \bigr) \, 
        ( dx\,\mathbf{i} + dy\,\mathbf{j} )  \notag\\
    &= \int_C f( x )\,dx  + \int_C g( y )\,dy 
        \label{eq:complex_int}
  \end{align}
\end{frame}

\end{document}

Answer 2

The font size in article and beamer are not the same. If you realy like to have one line equation in bemare, you need to use smaller fonts, for example scriptsize:

\documentclass[12pt]{beamer}
\usepackage{amsmath,amssymb,amsthm}

\begin{document}
My important one-line equation is:
  \begin{equation}\label{eq:1}\scriptsize
    \int_C {{\mathbf{F}}\left( {x,y} \right) \cdot d{\mathbf{r}}}  = \int_C {\left( {f\left( x \right){\mathbf{i}} + g\left( y \right){\mathbf{j}}} \right) \cdot \left( {dx{\mathbf{i}} + dy{\mathbf{j}}} \right)}  = \int_C {f\left( x \right)dx}  + \int_C {g\left( y \right)dy}
  \end{equation}
From (\ref{eq:q}) follows: \dots
\end{document}

To my opinion, the result is not so nice as at @Mico answer.