List of Equations / Table of Equations

Here's a modified version of Lev Bishop's code; I used the xstring package to remove the string "eq:" from the labels:

\documentclass[english]{article}
\setcounter{secnumdepth}{2}
\setcounter{tocdepth}{2}
\usepackage{amsmath}
\usepackage{tocloft}
\usepackage{xstring}
\usepackage[unicode=true, pdfusetitle,
 bookmarks=true,bookmarksnumbered=false,bookmarksopen=false,
 breaklinks=false,pdfborder={0 0 0},backref=false,colorlinks=false]
 {hyperref}

\makeatletter
\numberwithin{equation}{section}

% we use this for our refernces as well
\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}

% redefinition of \equation for convenience
\let\oldequation = \equation
\let\endoldequation = \endequation
\AtBeginDocument{\let\oldlabel = \label}% \AtBeginDocument because hyperref redefines \label
\newcommand{\mynewlabel}[1]{%
  \StrBehind{#1}{eq:}[\Str]% remove "eq:" from labels
  \myequations{\Str}\oldlabel{#1}}
  \renewenvironment{equation}{%
  \oldequation
  \let\label\mynewlabel
}{\endoldequation}

\newcommand{\listequationsname}{List of Equations}
\newlistof{myequations}{equ}{\listequationsname}
\newcommand{\myequations}[1]{%
      \addcontentsline{equ}{myequations}{\protect\numberline{\theequation}#1}}
\setlength{\cftmyequationsnumwidth}{3em}

\makeatother

\begin{document}
\tableofcontents
\listofmyequations

\section{Brushless Motor Fundamentals}
\subsubsection{DC Motor Operation}
Torque is generated in DC motors from the magnetic force,
also known as the Lorentz force, which is produced when an
electric current is passed through a coil in a magnetic field.
This force is given by \ref{eq:Force}.
\begin{equation}
  F=q[E+(v\times B)]
  \label{eq:Force}
\end{equation}
where $F$ is the force perpendicular to the coil,
$E$ is the electric field in the coil,
$v$ is the velocity of the charged particles in the coil,
and $B$ is the magnetic field. From mechanics, torque is
\begin{equation}
  \tau=F\times r
  \label{eq:Torque}
\end{equation}
If the electrical force in \ref{eq:Force} is ignored,
and the remaining magnetic force is used in \ref{eq:Torque},
with the assumption that $v$ is perpendicular to $B$, we find that
\begin{equation}
      \tau=qvBrsin\theta
  \label{eq:Magnetic}
\end{equation}

\end{document}

Here is a modified version of your example. The main change is that I redefine \label within equation environments:

\documentclass[english]{article}
\setcounter{secnumdepth}{2}
\setcounter{tocdepth}{2}
\usepackage{amsmath}
\usepackage[unicode=true, pdfusetitle,
 bookmarks=true,bookmarksnumbered=false,bookmarksopen=false,
 breaklinks=false,pdfborder={0 0 0},backref=false,colorlinks=false]
 {hyperref}

\makeatletter
\numberwithin{equation}{section}

% we use this for our refernces as well
\AtBeginDocument{\renewcommand{\ref}[1]{\mbox{\autoref{#1}}}}

% redefinition of \equation for convenience
\let\oldequation = \equation
\let\endoldequation = \endequation
\AtBeginDocument{\let\oldlabel = \label}% \AtBeginDocument because hyperref redefines \label
\newcommand{\mynewlabel}[1]{\myequations{#1}\oldlabel{#1}}
\renewenvironment{equation}{%
\oldequation
\let\label\mynewlabel
}{\endoldequation}

% try to make a List of Equations,
% error is most likely in the @currentlabelname above
\usepackage{tocloft}
\newcommand{\listequationsname}{List of Equations}
\newlistof{myequations}{equ}{\listequationsname}
\newcommand{\myequations}[1]{%
\addcontentsline{equ}{myequations}{\protect\numberline{\theequation}#1}}
\setlength{\cftmyequationsnumwidth}{3em}

\makeatother

\begin{document}
\tableofcontents{}
\listofmyequations

\section{Brushless Motor Fundamentals}
\subsubsection{DC Motor Operation}
Torque is generated in DC motors from the magnetic force,
also known as the Lorentz force, which is produced when an
electric current is passed through a coil in a magnetic field.
This force is given by \ref{eq:Force}.

\begin{equation}
F=q[E+(v\times B)]
\label{eq:Force}
\end{equation}
where F is the force perpendicular to the coil,
E is the electric field in the coil,
v is the velocity of the charged particles in the coil,
and B is the magnetic field. From mechanics, torque is

\begin{equation}
\tau=F\times r\label{eq:Torque}\end{equation}
If the electrical force in \ref{eq:Force} is ignored,
and the remaining magnetic force is used in \ref{eq:Torque},
with the assumption that v is perpendicular to B, we find that
\begin{equation}
\tau=qvBrsin\theta
\label{eq:Magnetic}\end{equation}

\end{document} 

I expanded upon the previous answers to define a command that you can use like so:

\noteworthy{a^2 + b^2 = c^2}{Pythagorean theorem} 

And it will automatically label, reference, box, and list the equations that I consider noteworthy. I'm really happy with the result.

Note that the red squares just highlight hyperlinks, they're not visible on the pdf.

And then the equation is numbered, boxed, labelled with text (that matches the list of equations), and gets a label to allow us to reference it.

Minimum viable example:

\documentclass{article}
\usepackage{tocloft}    % for list of equations
\usepackage{ragged2e}   % to undo \centering
\usepackage{hyperref}   % to make references hyperlinks
\usepackage{glossaries} 

% define list of equations
\newcommand{\listequationsname}{\Large{List of Equations}}
\newlistof{myequations}{equ}{\listequationsname}
\newcommand{\myequations}[1]{
   \addcontentsline{equ}{myequations}{\protect\numberline{\theequation}#1}
}
\setlength{\cftmyequationsnumwidth}{2.3em}
\setlength{\cftmyequationsindent}{1.5em}

% command to box, label, reference, and 
% include noteworthy equation in list of equations
\newcommand{\noteworthy}[2]{
\begin{align} \label{#2} \ensuremath{\boxed{#1}} \end{align} 
\myequations{#2} \centering \small \textit{#2} \normalsize \justify }

\begin{document}

\listofmyequations \pagebreak

\noteworthy{P(\bigcup_{n=1}^n A_n) \leq \sum_{n=1}^n P(A_n)}{Boole's inequality}

Where the events $A_n$ are disjoint, then the inequality 
in equation \ref{Boole's inequality} becomes an equality.

\end{document}