Force upright Greek letters with isomath

You don't need the isomath package:

\DeclareMathSymbol{\Gamma}{\mathalpha}{operators}{0}
\DeclareMathSymbol{\Delta}{\mathalpha}{operators}{1}
\DeclareMathSymbol{\Theta}{\mathalpha}{operators}{2}
\DeclareMathSymbol{\Lambda}{\mathalpha}{operators}{3}
\DeclareMathSymbol{\Xi}{\mathalpha}{operators}{4}
\DeclareMathSymbol{\Pi}{\mathalpha}{operators}{5}
\DeclareMathSymbol{\Sigma}{\mathalpha}{operators}{6}
\DeclareMathSymbol{\Upsilon}{\mathalpha}{operators}{7}
\DeclareMathSymbol{\Phi}{\mathalpha}{operators}{8}
\DeclareMathSymbol{\Psi}{\mathalpha}{operators}{9}
\DeclareMathSymbol{\Omega}{\mathalpha}{operators}{10}

To get an italic Gamma, use \mathnormal{\Gamma}. Try

$\Gamma\mathnormal{\Gamma}\mathbf{\Gamma}$

The command \DeclareMathSymbol is used for assigning a meaning to characters or commands in math mode. The second argument contains the "kind" of symbol; \mathalpha means a symbol that obeys to the alphabet selection commands. The third argument is the alphabet used by default; the fourth is the slot in the font. All the standard declarations are in fontmath.ltx loaded at format creation time.

Notice that these declarations won't work if the default font encoding of the document is T1 instead of OT1, as operators refers to the ordinary Roman document font. One should define a new math alphabet, in this case.

How to do this when the document encoding is T1? One has to define a new symbol font:

\DeclareSymbolFont{otone}{OT1}{cmr}{m}{n}
\SetSymbolFont{bold}{otone}{OT1}{cmr}{m}{n}
\DeclareMathSymbol{\Gamma}{\mathalpha}{otone}{0}
\DeclareMathSymbol{\Delta}{\mathalpha}{otone}{1}
\DeclareMathSymbol{\Theta}{\mathalpha}{otone}{2}
\DeclareMathSymbol{\Lambda}{\mathalpha}{otone}{3}
\DeclareMathSymbol{\Xi}{\mathalpha}{otone}{4}
\DeclareMathSymbol{\Pi}{\mathalpha}{otone}{5}
\DeclareMathSymbol{\Sigma}{\mathalpha}{otone}{6}
\DeclareMathSymbol{\Upsilon}{\mathalpha}{otone}{7}
\DeclareMathSymbol{\Phi}{\mathalpha}{otone}{8}
\DeclareMathSymbol{\Psi}{\mathalpha}{otone}{9}
\DeclareMathSymbol{\Omega}{\mathalpha}{otone}{10}

Of course cmr can be changed into the document's main font family name, provided it contains Greek uppercase letters in its OT1 version; but it's just a matter of giving the correct slot numbers for the chosen font.

isomath was written to set the math style to an 'ISO math style', as the author of the package puts it. Essentially, this means that it will be possible to typeset Greek letters (and non-Greek ones, for that matter) as bold italics, to denote vectors and matrices according to the ISO standard. It is possible to have upright letters, too. isomath requires OML font encoding. The isomath documentation (2011-01-14) states:

Currently only the mathdesign package provides upright fonts in OML encoding.

So, this package also needs to be loaded in order to obtain the correct fonts. LaTeX may otherwise display entirely different characters.

An example based on code snippets from the package documentation could be:

\documentclass[12pt,a4paper]{article}
\usepackage[utopia]{mathdesign}
\usepackage[OMLmathrm,OMLmathbf]{isomath} % options define which alphabets will be loaded, i.e. if bold face font is not necessary, `OMLmathbf` can be ommitted.
\begin{document}
$\Gamma$ $\mathrm{\Gamma}$ $\mathbf{\Gamma}$ $\mathbfit{\Gamma}$

$\pi$ $\mathrm{\pi}$ $\mathbf{\pi}$ $\mathbfit{\pi}$
\end{document}

The output will be:

It seems that the definition of the new math alphabets by isomath can lead to an error. To circumvent this, load the package with the option reuseMathAlphabets.

Known incompatibilities: fourierpackage