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如何在投影仪中排版逐行显示的数学证明

tag-icon • tag-icon beamer math-mode amsmath pause
如何在投影仪中排版逐行显示的数学证明

我想显示数学结果的分步证明。我希望在amsmath的align环境中有步骤遵循其他步骤，但我想要\pause证明中每一行后面的幻灯片即一次展示一个步骤，以便我的学生不会因为看幻灯片而分心或感到困惑。

\documentclass{beamer}

\usepackage[protrusion,expansion,kerning,tracking,spacing]{microtype}

\usepackage[utf8]{inputenc}

\usepackage{multicol}

\usepackage{framed}

\usepackage{amsmath,amssymb,amsfonts}
\usepackage[T1]{fontenc}

\usepackage{xcolor}
\microtypecontext{spacing=nonfrench}
\nonfrenchspacing

\usetheme{Berkeley}

\usefonttheme{serif}

\begin{document}
    \section{Example 1}
    \begin{frame}[allowframebreaks]{\(u\)-substitution example}
        \begin{framed}
            Find the antiderivative of the function defined by \(f(x) = \frac{x}{\sqrt{x^2 + 4}}\).
        \end{framed}

        \begin{align}
            \intertext{Introduce the auxiliary variable $u$.}
            u &= x^2 + 4\\
            \intertext{Differentiate with respect to $x$.}
            \frac{du}{dx} &= 2x\\
            \intertext{Multiply through by the differential.}
            du &= 2x\,dx\\
            \intertext{Substitute $u$ into $f$.}
            f(x) &= \frac{x}{\sqrt{u}}\\
            \intertext{Substitute into antiderivative expression.}
            \int f(x)\,dx &= \int \frac{x}{\sqrt{u}}\,dx\\
            \intertext{Extract a constant.}
            &= \frac{1}{2}\int \frac{2x}{\sqrt{u}}\,dx
            \intertext{Rewrite differential in terms of $u$.}
            &= \frac{1}{2}\int \frac{1}{\sqrt{u}}\left(2x\,dx\right)\\
            &= \frac{1}{2}\int \frac{1}{\sqrt{u}}\,du
            \intertext{Apply the power rule for indefinite integration.}
            &= \frac{1}{2}\int u ^ {-\frac{1}{2}}\,du\\
            &= \frac{1}{2}\frac{\sqrt{u}}{1/2} + C\\
            &= \sqrt{u} + C
            \intertext{Substitute $u$.}
            \int f(x)\,dx &= \sqrt{x^2 + 4} + C
        \end{align}
    \end{frame}
\end{document}

答案1

您\uncover<x-y>很可能可以\uncover<+->自由使用（即“从这里开始揭开”）。它没有以任何方式影响格式。只需确保不要引入虚假空格（行尾是 (La)TeX 的空格，除非行以以 开头的注释结尾%，否则“受保护”行尾后的空格将被忽略）。例如，我会写类似的东西：

\uncover<+->{%
   This is a step in my proof%
}%
\uncover<+->{%
   , continued here.
}

这样，逗号前就不会出现多余的空格。

答案2

我不确定我是否理解了这个问题。看起来证明不能放在一张幻灯片上，但可以将第二行作为的参数，\uncover<2->{.....}将第三行作为的参数，\uncover<3->{...}依此类推。这是我最近发表的一次演讲中的一个实际框架：

\begin{frame}{Some properties of $G$ and $K$}

\begin{itemize}[<+->]

\item\hiblue{$G(D)$ is a subring of the perfect closure of the field of
fractions of $D$.}

\item\hiblue{The inner adjunction $R\to K(R)$ is an injection.}

\item\hiblue{The inner adjunction $R\to K(R)$ is epic in semiprime
rings.}

\item\hiblue{The induced $\spec(K(R))\to\spec(R)$ is a bijection.}


\end{itemize}

\uncover<5->{\hired{$K$ is {\bf domain reflective} if it takes
domains to domains.}}

\uncover<6->{$K_\fld$ is not domain reflective.}

\end{frame}

前四项也一一展示出来。

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