Add some mathematical terms

chapters/dae.tex

@@ -88,13 +88,11 @@ \chapter{Modelica DAE Representation}\label{modelica-dae-representation}
 \end{lstlisting}
 \end{example}
 
-The generated set of equations is used for simulation and other analysis
-activities. Simulation means that an initial value problem is solved,
-i.e., initial values have to be provided for the states $x$, \cref{initialization-initial-equation-and-initial-algorithm}.
-The equations define a DAE (Differential Algebraic Equations) which may
-have discontinuities, a variable structure and/or which are controlled
-by a discrete-event system. Such types of systems are called
-\emph{hybrid DAEs}. Simulation is performed in the following way:
+The generated set of equations is used for simulation and other analysis activities.
+Simulation means that an initial value problem is solved, i.e., initial values have to be provided for the states $x$, \cref{initialization-initial-equation-and-initial-algorithm}.
+The equations define a DAE\index{DAE} (Differential Algebraic Equations) which may have discontinuities, a variable structure and/or which are controlled by a discrete-event system.
+Such types of systems are called \firstuse{hybrid DAEs}\index{hybrid DAE}.
+Simulation is performed in the following way:
 \begin{enumerate}
 \item\label{perform-simulation-integrate}
   The DAE \eqref{eq:dae} is solved by a numerical integration method. In this

chapters/equations.tex

@@ -712,13 +712,9 @@ \section{Events and Synchronization}\label{events-and-synchronization}
 
 \section{Initialization, initial equation, and initial algorithm}\label{initialization-initial-equation-and-initial-algorithm}
 
-Before any operation is carried out with a Modelica model (e.g.,
-simulation or linearization), initialization takes place to assign
-consistent values for all variables present in the model. During this
-phase, also the derivatives (\lstinline!der!), and the pre-variables (\lstinline!pre!),
-are interpreted as unknown algebraic variables. The initialization uses
-all equations and algorithms that are utilized in the intended operation
-(such as simulation or linearization).
+Before any operation is carried out with a Modelica model (e.g., simulation or linearization), initialization takes place to assign consistent values for all variables present in the model.
+During this phase, called the \firstuse{initialization problem}\index{initialization problem}, also the derivatives (\lstinline!der!), and the pre-variables (\lstinline!pre!), are interpreted as unknown algebraic variables.
+The initialization uses all equations and algorithms that are utilized in the intended operation (such as simulation or linearization).
 
 The equations of a when-clause are active during initialization, if and only if they are explicitly enabled with \lstinline!initial()!, and only in one of the two forms
 \lstinline!when initial() then! or \lstinline!when {$\ldots$, initial(), $\ldots$} then! (and similarly for \lstinline!elsewhen! and algorithms see below).  In this case, the when-clause equations remain active during the