Fixed some spelling mistakes and inconsistent mathematical notations (#…

…1983)

docs/0___preamble.adoc

@@ -1,5 +1,5 @@
 The https://fmi-standard.org/[Functional Mock-up Interface (FMI)] is a free standard that defines a container and an interface to exchange dynamic models using a combination of XML files, binaries and C code, distributed as a ZIP file.
-[[MAP,MAP]]It is supported by https://fmi-standard.org/tools/[more than 170 tools] and maintained as a https://www.modelica.org/projects[Modelica Association Project] (MAP FMI).
+[[MAP,MAP]]It is supported by https://fmi-standard.org/tools/[more than 200 tools] and maintained as a https://www.modelica.org/projects[Modelica Association Project] (MAP FMI).
 https://github.com/modelica/fmi-standard/releases[Releases] and https://github.com/modelica/fmi-standard/issues[issues] can be found on https://github.com/modelica/fmi-standard[github.com/modelica/fmi-standard].
 
 {empty} +

docs/1___overview.adoc

@@ -43,13 +43,13 @@ The following features have been removed:
 
 * The asynchronous mode for FMUs known from FMI 2.0 CS: this mode was not supported by tools and it can be suitably replaced by Co-Simulation implementations that control the asynchronous computation of FMUs via separate processes/threads created for each FMU.
 
-* The FMI `fmi2SetRealInputDerivatives` function: replaced by enabling the setting of inputs in <<IntermediateUpdateMode>>.
+* The FMI function `fmi2SetRealInputDerivatives`: replaced by enabling the setting of inputs in <<IntermediateUpdateMode>>.
 
 Parallel to the new standard features, the FMI Design Community has improved the standard quality by:
 
 * modernizing the development methodology (e.g. moving to github and following the github process) and a text-based source format,
 
-* publishing the FMI Standard now primarily as html to support easier navigation within the document and viewing on a wider range of devices,
+* publishing the FMI Standard now primarily as HTML to support easier navigation within the document and viewing on a wider range of devices,
 
 * supplying a large set of continuously validated Reference FMUs, and
 
@@ -291,7 +291,7 @@ Allocator must free::
 All memory (and other resources) allocated by the FMU are freed (released) by the FMU.
 Likewise, resources allocated by the importer are released by the importer.
 +
-Reason: this helps to prevent memory leaks and runtime errors due to incompatible runtime environments for different components.
+Reason: This helps to prevent memory leaks and runtime errors due to incompatible runtime environments for different components.
 
 Immutable strings::
 All strings passed as arguments or returned are read-only and must not be modified by the receiver.

docs/2_1_common_math.adoc

@@ -26,20 +26,20 @@ An ordering is defined on latexmath:[\mathbb{\text{T}}] that leads to the notati
 |Description
 
 ^|latexmath:[t_1 < t_2]
-|latexmath:[(t_{\mathit{R1}},t_{\mathit{I1}}) < (t_{\mathit{R2}}, t_{\mathit{I2}})\ \Leftrightarrow \ t_{\mathit{R1}} < t_{\mathit{R2}}\ \textbf{or} \ t_{\mathit{R1}}= t_{\mathit{R2}} \ \textbf{and} \ t_{\mathit{I1}} < t_{\mathit{I2}}]
+|latexmath:[(t_{\mathit{R}\hspace{0.1em}1},t_{\mathit{I}\hspace{0.1em}1}) < (t_{\mathit{R}\hspace{0.1em}2}, t_{\mathit{I}\hspace{0.1em}2})\ \Leftrightarrow \ t_{\mathit{R}\hspace{0.1em}1} < t_{\mathit{R}\hspace{0.1em}2}\ \textbf{or} \ ( t_{\mathit{R}\hspace{0.1em}1}= t_{\mathit{R}\hspace{0.1em}2} \ \textbf{and} \ t_{\mathit{I}\hspace{0.1em}1} < t_{\mathit{I}\hspace{0.1em}2}] )
 |latexmath:[t_1] is before latexmath:[t_2]
 
 ^|latexmath:[t_1 = t_2]
-|latexmath:[(t_{\mathit{R1}},t_{\mathit{I1}}) = (t_{\mathit{R2}},t_{\mathit{I2}}) \ \Leftrightarrow  t_{\mathit{R1}}= t_{\mathit{R2}}\ \textbf{and} \ t_{\mathit{I1}} = t_{\mathit{I2}}]
+|latexmath:[(t_{\mathit{R}\hspace{0.1em}1},t_{\mathit{I}\hspace{0.1em}1}) = (t_{\mathit{R}\hspace{0.1em}2},t_{\mathit{I}\hspace{0.1em}2}) \ \Leftrightarrow  t_{\mathit{R}\hspace{0.1em}1}= t_{\mathit{R}\hspace{0.1em}2}\ \textbf{and} \ t_{\mathit{I}\hspace{0.1em}1} = t_{\mathit{I}\hspace{0.1em}2}]
 |latexmath:[t_1] is identical to latexmath:[t_2]
 
 ^|latexmath:[t^{+}]
-|latexmath:[{(t_R,t_I)}^{+} \Leftrightarrow (\lim_{\mathit{\epsilon \rightarrow 0}}{\left(t_R + \varepsilon \right),t_{\mathit{Imax}})}]
+|latexmath:[{(t_R,t_I)}^{+} \Leftrightarrow (\lim_{\mathit{\varepsilon \rightarrow 0}}{\left(t_R + \varepsilon \right),t_{\mathit{Imax}})}]
 |right limit at latexmath:[t].
 latexmath:[t_{\mathit{Imax}}] is the largest occurring integer index of super-dense time at this latexmath:[t_R]
 
 ^|latexmath:[^-t]
-|latexmath:[^{-}{(t_R,t_I)} \Leftrightarrow (\lim_{\mathit{\epsilon \rightarrow 0}}{\left( t_R - \varepsilon \right),0)}]
+|latexmath:[^{-}{(t_R,t_I)} \Leftrightarrow (\lim_{\mathit{\varepsilon \rightarrow 0}}{\left( t_R - \varepsilon \right),0)}]
 |left limit at latexmath:[t]
 
 ^|latexmath:[v^+(t)]
@@ -58,9 +58,9 @@ latexmath:[t_{\mathit{Imax}}] is the largest occurring integer index of super-de
 \end{cases}
 \Leftrightarrow
 \begin{cases}
- v(^-t) & \text{ during } v(\left( t_R, 0 \right)) \text{, v not clocked }  \\
- v(\left( t_R,t_I - 1 \right)) & \text{ for } v(\left( t_R,t_I \right)) \text{ with } I > 0  \text{, v not clocked } \\
- v \text{ at previous tick of k } & \text{ if } v \text{ for clocked variable } v \text{ of clock k}
+ v(^-t) & \text{ during } v(\left( t_R, 0 \right)) \text{, } v \text{ not clocked }  \\
+ v(\left( t_R,t_I - 1 \right)) & \text{ for } v(\left( t_R,t_I \right)) \text{ with } t_I > 0  \text{, } v \text{ not clocked } \\
+ v \text{ at previous tick of k } & \text{ if } v \text{ is a clocked variable of clock k}
 \end{cases}
 ]
 a|previous value