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Cell[CellGroupData[{
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Cell[TextData[StyleBox["Using the command Manipulate[...] we can turn a \
static computation or graph into a dynamic and sophisticated model. We can \
wrap Manipulate[...] around any Wolfram command to create an interactive \
model. We need to introduce a parameter that we want to manipulate and some \
bounds for that parameter. ", "Subsubsection",
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Cell[TextData[{
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 StyleBox[". They all use the command Manipulate[...]. You can browse by \
topic and see the available templates. You can then download the project as a \
.cdf, which means that you get an interactive version that you can run \
locally on your computer, or you can download the author code, which means \
that you get a notebook (.nb) with the necessary code to generate the model.",
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Cell["An Interactive Model", "Section",
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Cell["\<\
Example 1. Make an interactive model that computes n^2, for n in the interval \
[1,4].\
\>", "Subsection",
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Cell["Solution 1", "Subsubsection",
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Cell["\<\
If you click the plus sign at the end of the slider, you get a set of video \
controls. You can introduce a particular value of the parameter and hit Enter \
to jump to that value. When you do a presentation, you can also hide the \
Wolfram commands and show only the interactive model. Once an interactive \
model is created, you can copy and run the model in a new notebook. You do \
not need to copy the code, only the model.\
\>", "Text",
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We can also set a default value for n when we call Manipulate[..]. The \
example below assumes that n=3 is the default value.\
\>", "Text",
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Cell["We can indicate the domain of n in different ways!", "Subsubsection",
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We can indicate the domain of n in different ways (each way will generate a \
different type of control button, slider, popup menu, checkbox, etc.)\
\>", "Text",
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In the two examples below, n takes values between 1 and 4 in steps of 0.25 \
and respectively in steps of 1. The Manipulate command creates a slider. \
\>", "Text",
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Instead of incrementing n in steps of 1, we can enumerate the list of \
possible values for n. The Manipulate command will create a button for each \
possible value.\
\>", "Text",
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If the list of possible values for n is too large, then a drop - down list \
will be created.\
\>", "Text",
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If no interval for n is given, Manipulate will create an empty text box where \
you can type in the value for n, then click Enter to obtain the result .\
\>", "Text",
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Cell["\<\
Options for the controls can also be given within the specification for the \
variables. \
\>", "Subsubsection",
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 "The option setting ",
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 " attempts to use controls of the specified type. Possible control types \
include: Animator, Checkbox, CheckboxBar, ColorSetter, ColorSlider, \
InputField, Manipulator, PopupMenu, RadioButton or RadioButtonBar, Setter or \
SetterBar, Slider, Slider2D, TogglerBar, Trigger, and VerticalSlider, None. \
More information can be found in the ",
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Possible settings for position are Bottom, Left, Right, and Top. "
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Cell["\<\
Example 1. Make an interactive model that computes n^2, for n in the interval \
[1,4].\
\>", "Subsection",
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Cell[TextData[{
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 " ",
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not change the position of the slider",
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Cell. This happens because the variable temp has its value changed during the \
evaluation (temp =temp^2), even if the value of n has not changed."
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The function g is now a local variable, so it does not cause any extra \
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We can keep the function f global, without causing any reevaluations of \
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copy ONLY the output of Manipulate (that is, ONLY the interactive model, \
absolutely NO code) in the new notebook. Try changing the slider. What do you \
notice?"
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new notebook. Try it!"
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Example 2. Make an interactive model that draws a random directed graph with \
n vertices, for n between 4 and 7.\
\>", "Subsection",
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If we do not want the graphics to rescale every time we generate a new graph, \
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Cell["\<\
Example 3. Make an interactive model that draws the graphs of the functions \
cos(mx) and sin(nx), where m is a continuous parameter in the interval [1,2], \
and n a discrete parameter in the set {4,5,6,7}.\
\>", "Subsection",
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