如何使框架定理的脚注出现在页面底部？

Question

我最近学会了如何在显示数学表达式周围放置一个框架，现在我想在框架中的文本中添加脚注。但是，当我尝试这样做时，脚注出现在框架的底部；我希望它出现在页。另外，在这种情况下，默认脚注符号是“a”；我希望它改用数字（从 1 开始）。我该如何实现这两个目标？

以下是 MWE：

\documentclass[12pt]{article}
\usepackage[a4paper,bindingoffset=0.2in,%
left=.5in,right=.5in,top=.5in,bottom=.5in,%
footskip=.25in]{geometry}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amssymb}
\usepackage[framemethod=TikZ]{mdframed}

\begin{document}
    
%\maketitle
\mdfdefinestyle{MyFrame}{%
    linecolor=black,
    outerlinewidth=0.25pt,
    roundcorner=2pt,
    innertopmargin=\baselineskip,
    innerbottommargin=\baselineskip,
    innerrightmargin=20pt,
    innerleftmargin=20pt,
    backgroundcolor=white}

\begin{mdframed}[style=MyFrame]
    \textbf{Change of Variables Theorem (in $\mathbb{R}^3$):}
    \footnote{Jerrold E. Marsden and Anthony J. Tromba. 2003.%
    In Vector calculus. W.H. Freeman, 387.} 
    Let $D^*$ be an elementary region in $\mathbb{R}^3$, let 
    $\Phi(u,v,w) = (x(u,v,w),y(u,v,w),z(u,v,w))$ be a one-to-one 
    $C^1$ map from $D^*$ to $\mathbb{R}^3$, and let $D = \Phi(D^*)$.
    Then 
    \begin{equation*}
          \iiint\limits_{D} f(x,y,z) \, dx \,dy \, dz 
        = \iiint\limits_{D^*} f(x(u,v,w),y(u,v,w),z(u,v,w)) 
          \left| \frac{\partial(x,y,z)}{\partial(u,v,w)} \right| 
          \, du \, dv \, dw.
    \end{equation*}
\end{mdframed}
    
\end{document}

当前显示的内容如下：

Answer 1

为了获得期望的结果，调整代码的最明显方法如下：

\documentclass[12pt]{article}
\usepackage[a4paper,bindingoffset=0.2in,%
left=.5in,right=.5in,top=.5in,bottom=.5in,%
footskip=.25in]{geometry}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{mathrsfs}
\usepackage{amssymb}
\usepackage[framemethod=TikZ]{mdframed}
\usepackage{footnote}

\begin{document}
    
    %\maketitle
    \mdfdefinestyle{MyFrame}{%
        linecolor=black,
        outerlinewidth=0.25pt,
        roundcorner=2pt,
        innertopmargin=\baselineskip,
        innerbottommargin=\baselineskip,
        innerrightmargin=20pt,
        innerleftmargin=20pt,
        backgroundcolor=white}
    \savenotes
    \begin{mdframed}[style=MyFrame]
        \stepcounter{footnote}
    \renewcommand{\thempfootnote}{\arabic{footnote}}
        \textbf{Change of Variables Theorem (in $\mathbb{R}^3$):}\footnote{Jerrold E. Marsden and Anthony J. Tromba. 2003. In Vector calculus. W.H. Freeman, 387.} Let $D^*$ be an elementary region in $\mathbb{R}^3$, let $\Phi(u,v,w) = (x(u,v,w),y(u,v,w),z(u,v,w))$ be a one-to-one $C^1$ map from $D^*$ to $\mathbb{R}^3$, and let $D = \Phi(D^*)$. Then 
        \begin{equation*}
            \iiint\limits_{D} f(x,y,z) \, dx \,dy \, dz = \iiint\limits_{D^*} f(x(u,v,w),y(u,v,w),z(u,v,w)) \left| \frac{\partial(x,y,z)}{\partial(u,v,w)} \right| \, du \, dv \, dw.
        \end{equation*}
    \end{mdframed}
    \spewnotes
    
\end{document}

您将获得以下结果：