Bold for vectors, tensors, and matrices in mathematical formula (Springer journal)

Question

I am preparing to send a paper to springer journal, In (instructions for Authors-> Scientific style) there is an instruction said: Bold for vectors, tensors, and matrices. I used \bm to bold to do that:

\begin{equation}
\frac{d\bm{P}_k^-}{dt}=\bm{F}_x(\bm{m}_k^-(t),t,\bm{\theta})\bm{P}_k^- +\bm{P}_k^- \bm{F}_x^T(\bm{m}_k^-(t),t,\bm{\theta}) + \Sigma(\bm{m}_k^-(t),t,\bm{\theta})
\label{eq:Euler}
\end{equation}

I get :

but in springer journal the equation looks like:

How can I fix that?

Answer 1

You have to use mathbf to produce the upright math fonts.

Since they usually represent vectors, you can renew the \vec command.

Also I created a derivative operator \drv which prints an upright d (as a derivative sign) keeping the spacing (at least to its right) that is present in the text

Here an implementation

   \documentclass{article}
\usepackage{amsmath}
\renewcommand{\vec}[1]{\mathbf{#1}}
\DeclareRobustCommand*{\drv}{\mathop{}\!\mathrm{d}}
\begin{document}
\begin{equation}
\frac{\drv\vec{P}_k^-}{\drv t}=\vec{F}_x(\vec{m}_k^-(t),t,\vec{\theta})\vec{P}_k^- +\vec{P}_k^- \vec{F}_x^T(\vec{m}_k^-(t),t,\vec{\theta}) + \Sigma(\vec{m}_k^-(t),t,\vec{\theta})
\label{eq:Euler}
\end{equation}

\end{document}

Thanks to @GustavoMezzetti and @lblb for their insightful remarks

---

EDIT

Since the user asked, I provide a solution, which I don't know if optimal, concerning the bold math symbols.

The "normal" way in fact should be

1. Load bm and upgreek

2. Substitute the greek letter with its upshape, ie theta becomes uptheta

3. Call \bm{\uptheta} instead of vec

If one wants to keep the vec version, instead, has only to substitute theta with uptheta to obtain what he wants:

\documentclass{article}
\usepackage{amsmath,bm,mathtools,upgreek}
\renewcommand{\vec}[1]{\bm{\mathrm{#1}}}
\DeclareRobustCommand*{\drv}{\mathop{}\!\mathrm{d}}
\begin{document}
\begin{equation}
\frac{\drv\vec{P}_k^-}{\drv t}=\vec{F}_x(\vec{m}_k^-(t),t,\vec{\uptheta})\vec{P}_k^- +\vec{P}_k^- \vec{F}_x^T(\vec{m}_k^-(t),t,\vec{\uptheta}) + \Sigma(\vec{m}_k^-(t),t,\vec{\uptheta})
\label{eq:Euler}
\end{equation}

\end{document}