Added discussion of the smooth operator

This closes #187

Author: mtiller

CHANGELOG.md

@@ -13,10 +13,19 @@ This file collects the significant changes to the book since its initial public
   * Emphasized the use of equations over algorithms in discussion on
     hysteresis.
 
+  * Added padding and the end of the HTML body so page doesn't end abruptly
+
+  * Added discussion of the ``smooth`` operator (issue
+    [#188](https://github.com/xogeny/ModelicaBook/pull/188)
+
 #### Bug Fixes
 
   * Completed discussion of synchronous clock features in section on Sampling.
 
+  * Completed table that discusses the relationship between events and
+    various functions/operators (issue
+    [#187](https://github.com/xogeny/ModelicaBook/pull/187)
+
 ### Version 0.3.2
 
 #### Enhancements

ModelicaByExample/Functions/Polynomials/Differentiation2.mo

@@ -1,5 +1,5 @@
 within ModelicaByExample.Functions.Polynomials;
-model Differentiation2 "Model that differentiates a function using smooth"
+model Differentiation2 "Model that differentiates a function using derivative annotation"
   Real yf;
   Real yp;
   Real d_yf;

text/source/behavior/discrete/events.rst

@@ -52,6 +52,33 @@ should also be noted that even a simple variable assignment, *e.g.,*
 
 can trigger an event to be generated.
 
+Piecewise Constructions
+***********************
+
+There is an important special case when dealing with conditional
+expressions.  In some cases, it is useful to create an expression that
+is constructed piecewise.  For example,
+
+.. code-block:: modelica
+
+    x = if (x<0) then 0 else x^2;
+
+It is hard for a Modelica compiler to reliably determine that such a
+function is continuous or whether it has continuous derivatives.  For
+this reason, Modelica includes the ``smooth`` operator to explicitly
+express such conditions.  For example, using the ``smooth`` operator
+as follows:
+
+.. code-block:: modelica
+
+    x = smooth(if (x<0) then 0 else x^2, 2);
+
+indicates that the expression is continuous as is and will remain
+continuous if differentiated up to 2 times.  Of course, in this case
+the expression is continuous regardless of the number of
+differentiations.  But the ``smooth`` operator requires an upper bound
+to be specified.
+
 Events and Functions
 ^^^^^^^^^^^^^^^^^^^^
 
@@ -108,4 +135,6 @@ Function                 Description
 ``previous(x)``          During clock tick, value of ``x`` during previous clock tick
 ``hold(x)``              Anytime, value of ``x`` during previous clock tick
 ``sample(expr,clock)``   During clock tick, value of ``expr``
+``noEvent(expr)``        Suppresses events generated by ``expr``
+``smooth(expr,p)``       Indicates ``expr`` can be safely differentiated ``p`` times.
 ======================  ========================================================