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I know \mathcal{ABC...}, but can't seem to bold these - thanks for help - PMF

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You're going to need a font that contains bold calligraphic fonts. One possibility for fonts without it is to use the bm package.

\bm{\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}}
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2  
This also works for bolding greek letters in math mode, e.g. \bm{\alpha} – Martin Tapankov Sep 6 '10 at 15:46

You can define your own math alphabet that accesses the Computer Modern symbol font in its bold weight.

\documentclass{article}

\DeclareMathAlphabet\mathbfcal{OMS}{cmsy}{b}{n}

\begin{document}
$\mathcal{A}$ $\mathbfcal{A}$
\end{document}

Example

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Another option is to bite the bullet and use LuaTeX with OpenType math fonts. In Context mkiv you can use

\setupbodyfont[xits]

\starttext
${\bf\cal abc}$
\stoptext 

To get bold calligraphic fonts. As a bonus you get lowercase calligraphic as well. I am sure that unicode-math for lualatex has something similar.

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2  
Yep: \setmathfont{xits-math.otf}...$\mathbfcal{abc}$. Can be used in XeLaTeX or LuaLaTeX. – Will Robertson Sep 7 '10 at 4:34

In mathematical environment you may use \boldsymbol

here is my suggestion:

\documentclass[...]{...}
\usepackage{amsbsy,amsmath}
\newcommand{\bs}[1]{\boldsymbol{#1}}
\newcommand{\HH}{\bs{\mathcal{H}}}
\newcommand{\DD}{\bs{\mathcal{D}}}
\newcommand{\pd}[2]{\frac{\partial{#1}}{\partial{#2}}}
\begin{document}
$\nabla\times\HH-\pd{\DD}{t}=\bs{j}$
\end{document}
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