Difference between revisions of "PhasePortrait Flash Applet Sample Problem 1"

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<em>This sample problem shows how to use this versatile applet.</em>
 
<em>This sample problem shows how to use this versatile applet.</em>
 
</p>
 
</p>
  +
<p style="background-color:#93BED2;border:black solid 1px;padding:3px;">This applet and WeBWorK problem are based upon work supported by the National Science Foundation under Grant Number DUE-0941388.</p>
 
<p>
 
<p>
The images below show the applet embedded in a WeBWorK homework problem. Note that the darker gray rectangle in the middle shows context sensitive help. The second imagereflects the help shown when the mouse hovers over the phase line. The applet asks the student to draw a one-dimensional phase portrait for the given differential equation. The applet can then grade the students drawing. Drawing is accomplished by placing equilibrium points, right and left arrows, and a symbol for derivative undefined on the phase line.
+
The images below show the applet embedded in a WeBWorK homework problem. Note that the darker gray rectangle in the middle shows context sensitive help. The second image reflects the help shown when the mouse hovers over the phase line. The applet asks the student to draw a one-dimensional phase portrait for the given differential equation. The applet can then grade the student's drawing. Drawing is accomplished by placing equilibrium points, right and left arrows, and a symbol for derivative undefined on the phase line.</p>
  +
<p>
  +
The first image shows the homework problem unstarted. The second image shows the homework problem successfully completed.
 
<br>
 
<br>
 
[[File:phasePortraitprob11_1.jpg]]
 
[[File:phasePortraitprob11_1.jpg]]
Line 90: Line 91:
 
All of the tagging information exists to
 
All of the tagging information exists to
 
allow the problem to be easily indexed.
 
allow the problem to be easily indexed.
Because this is a sample problem there
 
  +
There is an on-line
isn't a textbook per se, and we've used
 
some default tagging values. There is an on-line
 
 
[http://hobbes.la.asu.edu/Holt/chaps-and-secs.html list of current chapter and section names] and a similar
 
[http://hobbes.la.asu.edu/Holt/chaps-and-secs.html list of current chapter and section names] and a similar
 
[http://hobbes.la.asu.edu/Holt/keywords.html list of keywords]. The list of keywords should be comma separated and quoted (e.g., KEYWORDS('calculus','derivatives')).
 
[http://hobbes.la.asu.edu/Holt/keywords.html list of keywords]. The list of keywords should be comma separated and quoted (e.g., KEYWORDS('calculus','derivatives')).
Line 114: Line 113:
 
|- style=" background-color:#ffffdd;"
 
|- style=" background-color:#ffffdd;"
 
| <pre>
 
| <pre>
TEXT(beginproblem());
 
 
 
#############################
 
#############################
 
# Setup
 
# Setup
Line 162: Line 159:
 
</pre>
 
</pre>
 
| <p>
 
| <p>
The phasePortrait.swf applet ...
 
  +
Using the mouse to place tokens on the phase line is not a precise process, so we set the tolerance to 0.1 (<code>tolerance => 0.1</code>) to allow for some error. <code>$varLabel = "x";</code> sets the function to x. When the student moves the mouse along the phase line 'x=[mouse location]' is displayed. We also set the minimum and maximum values of the phase line.
 
</p>
 
</p>
 
<p>
 
<p>
Line 168: Line 165:
 
</p>
 
</p>
 
<p>
 
<p>
...
 
  +
The <code>$arrow</code> variables are used by the applet when <code>$solutionState</code> is true to display the correct placement of the arrows.
  +
</p>
  +
<p>
  +
The <code>Context()</code> line adds possible strings that might be returned by the applet depending on the placement of arrows, equilibria, and undefined values on the phase line. WeBWorK receives a list from the applet and uses the list answer evaluator to assess the correctness of the student's response. Here the correct answer is a sink at 0, a source at <code>$smaller</code> and a sink at <code>$bigger</code> where <code>$smaller</code> and <code>$bigger</code> are defined earlier in this code block.
 
</p>
 
</p>
 
|- style=" background-color:#ccffff;"
 
|- style=" background-color:#ccffff;"
 
| <pre>
 
| <pre>
#######################################
+
###################################
# How to use the Graph_Test applet.
+
# Create link to applet
# Purpose: The purpose of this
+
###################################
# applet is to ask graphical
+
$appletName = "phasePortrait";
# limit questions
+
$applet = FlashApplet(
# Use of applet: The applet
+
codebase => findAppletCodebase("$appletName.swf"),
# state consists of the
+
appletName => $appletName,
# following fields:
+
appletId => $appletName,
# qType - question type: limits,
+
setStateAlias => 'setXML',
# continuity, first_derivative,
+
getStateAlias => 'getXML',
# second_derivative
+
setConfigAlias => 'setConfig',
# hintState - context sensitive
+
maxInitializationAttempts => 5, # number of attempts to initialize applet
# help is either on or off.
+
answerBoxAlias => 'answerBox',
# Generally turned on after
+
height => '400',
# dueDate
+
width => '550',
# problemSeed - the seed sets
+
bgcolor => '#e8e8e8',
# the random parameters that
+
debugMode => 0,
# control which graph is
+
submitActionScript =>
# chosen. If the seed is
+
qq{getQE("answerBox").value=getApplet("$appletName").getAnswer() },
# changed, the graph is
+
);
# changed.
 
#######################################
 
# qType = limits
 
# right_limits - returns a
 
# list of points (a,b)
 
# such that
 
# lim_{x\to a^-}f(x)=b,
 
# but
 
# lim_{x\to a^+}f(x)\= b
 
# left_limits - returns a
 
# list of points (a,b)
 
# such that
 
# lim_{x\to a^+}f(x)=b,
 
# but
 
# lim_{x\to a^-}f(x)\= b
 
# neither_limits - returns
 
# a list of points (a,b)
 
# such that
 
# lim_{x\to a^-}f(x)\=
 
# lim_{x\to a^+}f(x)\=
 
# f(a)=b
 
# get_intervals returns a
 
# list of intervals on
 
# which f(x) is continuous.
 
# get_f_of_x - given x value,
 
# returns f(x).
 
# returns NaN for x notin
 
# [-10,10].
 
# getf_list - given x value
 
# and string returns
 
# "function" - returns f(x)
 
# "leftlimit" - returns
 
# lim_{x->a^-}f(x)
 
# "rightlimit" - returns
 
# lim_{x->a^+}f(x)
 
# "limit" - returns
 
# lim_{x->a}f(x) or "DNE"
 
 
</pre>
 
</pre>
| <p>This is the <strong>Applet link section</strong> of the problem.
 
  +
| <p>
</p><br>
 
  +
This is the <strong>Applet link section</strong> of the problem.
  +
</p>
  +
<br>
 
<p>
 
<p>
 
Those portions of the code that begin
 
Those portions of the code that begin
Line 202: Line 204:
 
to your particular problem.
 
to your particular problem.
 
</p>
 
</p>
|- style=" background-color:#ccffff;"
 
  +
<p>You must include the section that
| <pre>
 
#
 
# What does the applet do?
 
# The applet draws a graph
 
# with jumps, a cusp and
 
# discontinuities
 
# When turned on, there is
 
# context sensitive help.
 
################################
 
############################
 
# Create link to applet
 
############################
 
$appletName = "Graph_Limit";
 
$applet = FlashApplet(
 
codebase
 
=> findAppletCodebase
 
("$appletName.swf"),
 
appletName
 
=> $appletName,
 
appletId
 
=> $appletName,
 
setStateAlias
 
=> 'setXML',
 
getStateAlias
 
=> 'getXML',
 
setConfigAlias
 
=> 'setConfig',
 
maxInitializationAttempts
 
=> 10,
 
height
 
=> '475',
 
width
 
=> '425',
 
bgcolor
 
=> '#e8e8e8',
 
debugMode
 
=> 0,
 
submitActionScript
 
=> qq{
 
getQE("func").value=getApplet
 
("$appletName").getf_list($x1,"function");
 
getQE("rlimit").value=getApplet
 
("$appletName").getf_list($x2,"rightlimit");
 
getQE("llimit").value=getApplet
 
("$appletName").getf_list($x3,"leftlimit");
 
getQE("limit").value=getApplet
 
("$appletName").getf_list($x4,"limit");
 
},
 
);
 
</pre>
 
| <p>You must include the section that
 
 
follows <code># Create link to
 
follows <code># Create link to
 
applet</code>. If you are embedding
 
applet</code>. If you are embedding
a different applet, from the Graph_Limit
+
a different applet, from the phasePortrait
 
applet, put your applet name in place of
 
applet, put your applet name in place of
'Graph_Limit' in the line <code>$appletName =</code>
+
'phasePortrait' in the line <code>$appletName =</code>
<code> "Graph_Limit";</code>.
+
<code> "phasePortrait";</code>.
 
Enter the height of the applet
 
Enter the height of the applet
in the line <code>height => '475',</code>
+
in the line <code>height => '400',</code>
in place of 475 and the width in the line
+
in place of 400 and the width in the line
<code>width => '425',</code> in place of 425.
+
<code>width => '550',</code> in place of 550.
 
</p><br>
 
</p><br>
   
<p>The code <code>qq{ </code><code>
 
getQE("func").value=getApplet</code>
 
<code>("$appletName").getf_list($x1,"function");</code><code>
 
getQE("rlimit").value=getApplet</code>
 
<code>("$appletName").getf_list($x2,"rightlimit");</code><code>
 
getQE("llimit").value=getApplet</code>
 
<code>("$appletName").getf_list($x3,"leftlimit");</code><code>
 
getQE("limit").value=getApplet</code>
 
<code>("$appletName").getf_list($x4,"limit");</code><code>
 
}</code>
 
is called when the 'Submit Answers'
 
button in the problem is pressed.
 
There is an external interface function
 
designed inside the applet. The function
 
name is 'getf_list'. These lines of code
 
call the function with javascript.
 
<code>getf_list</code>, takes two arguments:
 
the x-coordinate of a point, and a string
 
value. The string may be any of the
 
following four alternatives: "function",
 
"rightlimit", "leftlimit", "limit".
 
<code>getf_list</code> returns either
 
the value of the function at the x-coordinate,
 
or the specified limit. The line <code>
 
getQE("func").value=getApplet</code>
 
<code>("$appletName").getf_list($x1,"function");</code>
 
gets the value of the function at <code>$x1</code>
 
and stores this value in the hidden javascript
 
form field named "func".</p>
 
 
|- style=" background-color:#ccffff;"
 
|- style=" background-color:#ccffff;"
 
| <pre>
 
| <pre>
Line 300: Line 222:
 
# Configure applet
 
# Configure applet
 
###################################
 
###################################
# configuration consists of
 
  +
$config_string = <<"ENDCONFIG";
# hintState, question type, and
 
  +
<XML>
# random seed, and x-coordinates of
 
  +
<leng>400</leng>
# four points where jumps,
 
  +
<vari>$varLabel</vari>
# discontinuities or cusps
 
  +
<xmin>$xmin</xmin>
# occur.
 
  +
<xmax>$xmax</xmax>
$applet->configuration(qq{<xml>
 
  +
<showSolution>$showSolution</showSolution>
<hintState>$hintState</hintState>
 
  +
<solutionPts>
<qtype>limits</qtype>
 
  +
<aPicon lrn='$arrow1dir' loc='$arrow1'></aPicon>
<seed>$problemSeed</seed>
 
  +
<aPicon lrn='n' loc='0'></aPicon>
<xlist x1='$x1' x2='$x2'
 
  +
<aPicon lrn='$arrow2dir' loc='$arrow2'></aPicon>
x3='$x3' x4='$x4' /></xml>});
 
  +
<aPicon lrn='n' loc='$smaller'></aPicon>
$applet->initialState(qq{<xml>
 
  +
<aPicon lrn='$arrow3dir' loc='$arrow3'></aPicon>
<hintState>$hintState</hintState>
 
  +
<aPicon lrn='n' loc='$bigger'></aPicon>
<qtype>limits</qtype>
 
  +
<aPicon lrn='$arrow4dir' loc='$arrow4'></aPicon>
<seed>$problemSeed</seed>
 
  +
</solutionPts>
<xlist x1='$x1' x2='$x2'
 
  +
</XML>
x3='$x3' x4='$x4' /></xml>});
 
  +
ENDCONFIG
 
TEXT( MODES(TeX=>'object code',
 
HTML=>$applet->insertAll(
 
debug=>0,
 
includeAnswerBox=>0,
 
)));
 
 
TEXT(MODES(TeX=>"", HTML=><<'END_TEXT'));
 
<input type="hidden"
 
name="func" id="func" />
 
<input type="hidden"
 
name="llimit" id="llimit" />
 
<input type="hidden"
 
name="rlimit" id="rlimit" />
 
<input type="hidden"
 
name="limit" id="limit" />
 
END_TEXT
 
 
$answerString1 =
 
$inputs_ref->{func};
 
my $correctAnswer1 =
 
Compute("$answerString1");
 
 
$answerString2 =
 
$inputs_ref->{rlimit};
 
my $correctAnswer2 =
 
Compute("$answerString2");
 
 
$answerString3 =
 
$inputs_ref->{llimit};
 
my $correctAnswer3 =
 
Compute("$answerString3");
 
 
$answerString4 =
 
$inputs_ref->{limit};
 
my $correctAnswer4 =
 
Compute("$answerString4");
 
   
  +
$applet->configuration($config_string);
  +
$applet->initialState($config_string);
   
 
</pre>
 
</pre>
| <p> The lines <code>$applet->configuration</code>
 
  +
| <p> This configuration information is sent to the applet to set it up. <code>leng</code> sets the length in pixels of the phase line. <code>vari</code> sets the variable name. The default is y; we have set it to x here. We set the minimum and maximum values of the phase line. The defaults are -10 and 10. The default for <code>showSolution</code> is false. We set it to true when the <code>dueDate</code> has passed. <code>solutionPts</code> values are only used if <code>showSolution</code> is true. <code>aPicon</code> are tokens that will be placed on the phase line when the due date is past. <code>lrn</code> takes four possible values: 'l' for left arrow, 'r' for right arrow, 'n' for node or equilibrium point, and 'u' for undefined value of the derivative. <code>loc</code> provides the location of the token on the phase line.
<code>(qq{<xml><hintState>$hintState</hintState></code>
 
<code><qtype>$qtype</qtype></code>
 
<code><seed>$problemSeed</seed></code>
 
<code><xlist x1='$x1' x2='$x2'</code>
 
<code> x3='$x3' x4='$x4' /></code>
 
<code></xml>});</code> and <code>$applet</code>
 
<code>->initialState</code><code>(qq{<xml></code>
 
<code><hintState>$hintState</hintState></code>
 
<code><qtype>$qtype</qtype></code><code><seed>$problemSeed</seed></code>
 
<code><xlist x1='$x1' x2='$x2'</code><code> x3='$x3' x4='$x4' /></code>
 
<code></xml>});</code> configure the applet.
 
The configuration of the applet is done in xml.
 
The hintState is set to the variable
 
<code>$hintState</code>, the question type is set to
 
<code>$qtype</code> and the problem seed is the
 
WeBWorK environmental variable <code>$problemSeed</code>.
 
The variables <code>$x1</code>, <code>$x2</code>,
 
<code>$x3</code> and <code>$x4</code> are also
 
passed to the applet.
 
</p><br>
 
<p>
 
The hidden form fields are created in the code block:
 
<code>
 
TEXT(MODES(TeX=>"", HTML=><<'END_TEXT'));
 
<input type="hidden"</code>
 
<code> name="func" id="func" /></code>
 
<code>
 
<input type="hidden"</code>
 
<code> name="llimit" id="llimit" /></code>
 
<code>
 
<input type="hidden"</code>
 
<code> name="rlimit" id="rlimit" /></code>
 
<code>
 
<input type="hidden"</code>
 
<code> name="limit" id="limit" /></code>
 
<code>
 
END_TEXT
 
</code>
 
The line <code>TEXT(MODES(TeX=>"", HTML=><<'END_TEXT'));</code>
 
prevents the hidden fields from becoming part of the hard copy.
 
</p><br>
 
 
<p>
 
<code>TEXT( MODES(TeX=>'object code',</code>
 
<code> HTML=>$applet->insertAll(</code>
 
<code>
 
debug=>0,</code>
 
<code>
 
includeAnswerBox=>0,</code>
 
<code>
 
reinitialize_button=>$permissionLevel>=10,</code>
 
<code>
 
)));</code> actually embeds the applet
 
in the WeBWorK problem.
 
</p><br>
 
<p>When the submit button is pressed, the
 
hidden form fields defined in this block are
 
filled with information from the applet.
 
 
</p>
 
</p>
<p>
 
The data from the hidden form fields is used
 
in these simple perl subroutines to define the
 
correct answers to the four questions that are
 
part of this WeBWorK problem.</p>
 
<p>The WeBWorK variable $answerString1 is the
 
content of the hidden form field "func".
 
$correctAnswer1 is the solution to the first
 
question. The solutions for the next two
 
questions are defined in a similar way.
 
The final question also has 'DNE' as a possible
 
correct answer for the student to enter. The
 
way that the applet is designed, the left and
 
right limits always exist.</p>
 
 
|- style=" background-color:#ccffff;"
 
|- style=" background-color:#ccffff;"
 
| <pre>
 
| <pre>
Line 450: Line 265:
 
|- style=" background-color:#ffdddd;"
 
|- style=" background-color:#ffdddd;"
 
| <pre>
 
| <pre>
  +
#############################
  +
# Main text
  +
#############################
  +
TEXT(beginproblem());
  +
  +
Context()->texStrings;
 
BEGIN_TEXT
 
BEGIN_TEXT
 
  +
Use the applet provided to draw a phase portrait for \( \displaystyle x^\prime = -$c x($a-x)($b-x) \).
 
$BR
 
$BR
The graph shown is for the
 
  +
The above equation could represent a model of a population that can
function \(f(x)\).
 
  +
become extinct if it drops below a particular critical value.
$BR Compute the following
 
  +
$BR$BR
quantities:
 
  +
What is this critical value? \{ ans_rule(10) \}
 
$BR
 
$BR
a)
 
\(f($x1)=\)
 
\{ans_rule(35) \}
 
$BR
 
b)
 
\(\lim_{x\to {$x2}^+}f(x)=\)
 
\{ans_rule(35) \}
 
   
$BR
 
  +
END_TEXT
c)
 
\(\lim_{x\to {$x3}^-}f(x)=\)
 
\{ans_rule(35) \}
 
   
$BR
 
  +
# Insert applet
d)
 
\(\lim_{x\to {$x4}}f(x)=\)
 
\{ans_rule(35) \}
 
   
$BR
 
  +
TEXT( MODES(TeX=>'A graph appears here in the html version.',
END_TEXT
 
  +
HTML=>$applet->insertAll(debug=>0,includeAnswerBox=>1)));
 
Context()->normalStrings;
 
Context()->normalStrings;
 
</pre>
 
</pre>
Line 502: Line 310:
 
<p>
 
<p>
 
There are a number of variables that set
 
There are a number of variables that set
formatting: <code>$PAR</code> is a paragraph
+
formatting: <code>$BR</code> is a break (like <code><BR></code> in HTML). Here, <code>ans_rule(10)</code>
break (like <code>\par</code> in TeX).
+
is a function that inserts an answer blank 10
[[FormatVariableList|This page]] gives a list
 
of variables like this. Finally, <code>\{&nbsp;\}</code>
 
sets off <em>code that will be executed
 
in the problem text</em>. Here, <code>ans_rule(35)</code>
 
is a function that inserts an answer blank 35
 
 
characters wide.
 
characters wide.
 
</p>
 
</p>
 
|- style=" background-color:#eeccff;"
 
|- style=" background-color:#eeccff;"
 
| <pre>
 
| <pre>
#############################
+
############################
#
 
 
# Answers
 
# Answers
#
 
  +
############################
## answer evaluators
 
   
ANS( $correctAnswer1->cmp() );
 
  +
$showPartialCorrectAnswers = 1;
#checks AnSwEr00001
 
  +
Context()->{error}{msg}
ANS( $correctAnswer2->cmp() );
 
  +
{"'one' is not defined in this context"} =
#checks AnSwEr00002
 
  +
"You have not placed equilibrium points and arrows on the phase line.";
ANS( $correctAnswer3->cmp() );
 
  +
Context()->{error}{msg}
#checks AnSwEr00003
 
  +
{"'two' is not defined in this context"} =
ANS(num_cmp($correctAnswer4,
 
  +
"You must have an arrow before the first equililbrium point.";
strings=>['DNE']));
 
  +
Context()->{error}{msg}
#checks AnSwEr00004
 
  +
{"'three' is not defined in this context"} =
  +
"You must have an arrow after the last equilibrium point.";
  +
Context()->{error}{msg}
  +
{"'four' is not defined in this context"} =
  +
"Two consecutive arrows must point in the same direction.";
  +
Context()->{error}{msg}
  +
{"'five' is not defined in this context"} =
  +
"There must be an arrow between equilibrium points.";
  +
Context()->{error}{msg}
  +
{"'six' is not defined in this context"} =
  +
"There must be an arrow between an equilibrium point and derivative undefined point.";
  +
Context()->{error}{msg}
  +
{"'seven' is not defined in this context"} =
  +
"There must be an arrow between an equilibrium point and derivative undefined point.";
  +
Context()->{error}{msg}
  +
{"'eight' is not defined in this context"} =
  +
"There must be an arrow between derivative undefined points.";
   
  +
NAMED_ANS( 'answerBox'=>$anslist->cmp(ordered=>1));
  +
ANS( Compute("$smaller")->cmp());
   
ENDDOCUMENT();
 
  +
COMMENT("MathObject version.");
  +
  +
ENDDOCUMENT();
 
</pre>
 
</pre>
 
| <p>
 
| <p>
 
This is the <strong>answer</strong>
 
This is the <strong>answer</strong>
 
section of the problem. The problem answer
 
section of the problem. The problem answer
is set by the <code>ANS( $correctAnswer1->cmp() );</code>,
+
is set by the <code>NAMED_ANS( 'answerBox'=>$anslist->cmp(ordered=>1));</code>, and
<code>ANS( $correctAnswer2->cmp() );</code>,
+
<code>ANS( Compute("$smaller")->cmp());</code> lines. The <code>NAMED_ANS</code> line checks the correctness of the student's work using the applet. The applet returns a list. The ordered list answer checker is used to assess correctness.
<code>ANS( $correctAnswer3->cmp() );</code>,
 
and <code>ANS(num_cmp</code>
 
<code>($correctAnswer4,</code>
 
<code>strings=>['DNE']));</code> lines.
 
These compare the student's answer with the
 
answers returned from the applet. Answers 1-3
 
follow the same basic structure. The fourth
 
answer allows for either a numeric answer or
 
the string 'DNE' for limits that do not exist.
 
 
</p>
 
</p>
 
<p>
 
<p>
Line 536: Line 363:
 
becomes available when the due date has passed.
 
becomes available when the due date has passed.
 
</p>
 
</p>
  +
<p>The lines that begin <code>Context()->{error}{msg}</code> redefine error messages to messages that are specific to the phasePortrait applet. For example, it makes no sense to have consecutive arrows pointing different directions on a phase portrait so an appropriate error is returned.</p>
 
<p>
 
<p>
 
The <code>ENDDOCUMENT();</code> command is the
 
The <code>ENDDOCUMENT();</code> command is the
Line 541: Line 369:
 
</p>
 
</p>
 
|}
 
|}
  +
  +
  +
[[Category:Applets]]
  +
[[Category:Flash Applets]]

Latest revision as of 12:32, 12 June 2013

Flash Applets embedded in WeBWorK questions phasePortrait Example

Page Under Construction

Sample Problem with phasePortrait.swf embedded

This sample problem shows how to use this versatile applet.

This applet and WeBWorK problem are based upon work supported by the National Science Foundation under Grant Number DUE-0941388.

The images below show the applet embedded in a WeBWorK homework problem. Note that the darker gray rectangle in the middle shows context sensitive help. The second image reflects the help shown when the mouse hovers over the phase line. The applet asks the student to draw a one-dimensional phase portrait for the given differential equation. The applet can then grade the student's drawing. Drawing is accomplished by placing equilibrium points, right and left arrows, and a symbol for derivative undefined on the phase line.

The first image shows the homework problem unstarted. The second image shows the homework problem successfully completed.
PhasePortraitprob11 1.jpg PhasePortraitprob11 2.jpg

A standard WeBWorK PG file with an embedded applet has six sections:

  1. A tagging and description section, that describes the problem for future users and authors,
  2. An initialization section, that loads required macros for the problem,
  3. A problem set-up section that sets variables specific to the problem,
  4. An Applet link section that inserts the applet and configures it, (this section is not present in WeBWorK problems without an embedded applet)
  5. A text section, that gives the text that is shown to the student, and
  6. An answer and solution section, that specifies how the answer(s) to the problem is(are) marked for correctness, and gives a solution that may be shown to the student after the problem set is complete.

The sample file attached to this page shows this; below the file is shown to the left, with a second column on its right that explains the different parts of the problem that are indicated above. A screenshot of the applet embedded in this WeBWorK problem is shown below:

There are other example problems using this applet:
GraphLimit Flash Applet Sample Problem 2
And other problems using applets:
Derivative Graph Matching Flash Applet Sample Problem
GraphSketch Flash Applet Sample Problem 1
USub Applet Sample Problem
trigwidget Applet Sample Problem
solidsWW Flash Applet Sample Problem 1
solidsWW Flash Applet Sample Problem 2
solidsWW Flash Applet Sample Problem 3
Hint Applet (Trigonometric Substitution) Sample Problem
Other useful links:
Flash Applets Tutorial
Things to consider in developing WeBWorK problems with embedded Flash applets

PG problem file Explanation
## DESCRIPTION
## First order ODEs: phase portraits
## ENDDESCRIPTION

## KEYWORDS('differential equations','first order','phase portraits','Flash applets','NSF-0941388')

## DBsubject('Differential Equations')
## DBchapter('First Order Differential Equations')
## DBsection('Phase Portraits')
## Date('02/14/2013')
## Author('Barbara Margolius')
## Author('Felipe Martins')
## Institution('Cleveland State University')
## TitleText1('A Modern Introduction to Differential Equations')
## EditionText1('2009')
## AuthorText1('Ricardo')
## Section1('2.5')
## Problem1('A11')
###########################################
# This work is supported in part by 
# the National Science Foundation 
# under the grant DUE-0941388.
###########################################

This is the tagging and description section of the problem. Note that any line that begins with a "#" character is a comment for other authors who read the problem, and is not interpreted by WeBWorK.

The description is provided to give a quick summary of the problem so that someone reading it later knows what it does without having to read through all of the problem code.

All of the tagging information exists to allow the problem to be easily indexed. There is an on-line list of current chapter and section names and a similar list of keywords. The list of keywords should be comma separated and quoted (e.g., KEYWORDS('calculus','derivatives')).

DOCUMENT(); 

loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"AppletObjects.pl",
);

This is the initialization section of the problem. The first executed line of the problem must be the DOCUMENT(); command. Note that every command must end with a semicolon.

The loadMacros command loads information that works behind the scenes. For our purposes we can usually just load the macros shown here and not worry about things further.

#############################
#  Setup
#############################

Context("Numeric");
Context()->flags->set(
  tolerance => 0.1,
  tolType => "absolute",
);

$a=random(1,4,1);
$b=random(1,4,1);
if($b==$a){
  $b++;
}
$varLabel = "x";
$smaller = $b;
$bigger = $a;
if($a<$b){
  $smaller = $a;
  $bigger = $b;
}

$c=random(2,5,1);

$xmin = Compute("-$bigger-2");
$xmax = Compute("$bigger+2");

$showSolution = false;
if(time>$dueDate){
  $showSolution=true;
}

$arrow1 = Compute("($xmin)/2");
$arrow2 = Compute("($smaller)/2");
$arrow3 = Compute("($smaller+$bigger)/2");
$arrow4 = Compute("($xmax+$bigger)/2");
$arrow1dir = "r";
$arrow2dir = "l";
$arrow3dir = "r";
$arrow4dir = "l";

Context()->strings->add(sink=>{},source=>{},node=>{},inc=>{},dec=>{},all=>{},usource=>{},usink=>{});
$anslist = List("sink",Compute("0"),"source",Compute("$smaller"),"sink",Compute("$bigger"));

Using the mouse to place tokens on the phase line is not a precise process, so we set the tolerance to 0.1 (tolerance => 0.1) to allow for some error. $varLabel = "x"; sets the function to x. When the student moves the mouse along the phase line 'x=[mouse location]' is displayed. We also set the minimum and maximum values of the phase line.

The applet has solution information embedded in it. When $solutionState=false, this information is not shown. When $solutionState=true, this information is revealed. The time parameter tracks the current date and time. The conditional compares that to the due date for the problem set (in the $dueDate scalar variable) and sets $solutionState to true if the due date has passed and leaves $solutionState set to false if the assignment is not yet due.

The $arrow variables are used by the applet when $solutionState is true to display the correct placement of the arrows.

The Context() line adds possible strings that might be returned by the applet depending on the placement of arrows, equilibria, and undefined values on the phase line. WeBWorK receives a list from the applet and uses the list answer evaluator to assess the correctness of the student's response. Here the correct answer is a sink at 0, a source at $smaller and a sink at $bigger where $smaller and $bigger are defined earlier in this code block.

###################################
# Create  link to applet 
###################################
    $appletName = "phasePortrait";
    $applet =  FlashApplet(
       codebase              => findAppletCodebase("$appletName.swf"),
       appletName            => $appletName,
       appletId              => $appletName,
       setStateAlias         => 'setXML',
       getStateAlias         => 'getXML',
       setConfigAlias        => 'setConfig',
       maxInitializationAttempts => 5,   # number of attempts to initialize applet
       answerBoxAlias        => 'answerBox',
       height                => '400',
       width                 => '550',
       bgcolor               => '#e8e8e8',
       debugMode             =>  0,
       submitActionScript  =>  
  qq{getQE("answerBox").value=getApplet("$appletName").getAnswer() },
     );

This is the Applet link section of the problem.


Those portions of the code that begin the line with # are comments and can be omitted or replaced with comments appropriate to your particular problem.

You must include the section that follows # Create link to applet. If you are embedding a different applet, from the phasePortrait applet, put your applet name in place of 'phasePortrait' in the line $appletName = "phasePortrait";. Enter the height of the applet in the line height => '400', in place of 400 and the width in the line width => '550', in place of 550.


###################################
# Configure applet
###################################
$config_string = <<"ENDCONFIG";
<XML>
    <leng>400</leng>
    <vari>$varLabel</vari>
    <xmin>$xmin</xmin>
    <xmax>$xmax</xmax>
    <showSolution>$showSolution</showSolution>
    <solutionPts>
         <aPicon lrn='$arrow1dir' loc='$arrow1'></aPicon>
         <aPicon lrn='n' loc='0'></aPicon>
         <aPicon lrn='$arrow2dir' loc='$arrow2'></aPicon>
         <aPicon lrn='n' loc='$smaller'></aPicon>
         <aPicon lrn='$arrow3dir' loc='$arrow3'></aPicon>
         <aPicon lrn='n' loc='$bigger'></aPicon>
         <aPicon lrn='$arrow4dir' loc='$arrow4'></aPicon>
     </solutionPts>
</XML>
ENDCONFIG

$applet->configuration($config_string);
$applet->initialState($config_string);

This configuration information is sent to the applet to set it up. leng sets the length in pixels of the phase line. vari sets the variable name. The default is y; we have set it to x here. We set the minimum and maximum values of the phase line. The defaults are -10 and 10. The default for showSolution is false. We set it to true when the dueDate has passed. solutionPts values are only used if showSolution is true. aPicon are tokens that will be placed on the phase line when the due date is past. lrn takes four possible values: 'l' for left arrow, 'r' for right arrow, 'n' for node or equilibrium point, and 'u' for undefined value of the derivative. loc provides the location of the token on the phase line.

TEXT(MODES(TeX=>"", HTML=><<'END_TEXT'));
<script>
if (navigator.appVersion.indexOf("MSIE") > 0) {
    document.write("<div width='3in' 
    align='center' style='background:yellow'>
    You seem to be using Internet Explorer.
    <br/>It is recommended that another 
    browser be used to view this page.</div>");
}
</script>
END_TEXT

The text between the <script> tags detects whether the student is using Internet Explorer. If the student is using this browser, a warning is issued and the student is advised to use another browser. IE mis-sizes the applets. Some will work correctly when displayed at the wrong size, but others will fail. We do not recommend using IE with WeBWorK problems with Flash embedded.

#############################
#  Main text
#############################
TEXT(beginproblem());

Context()->texStrings;
BEGIN_TEXT
Use the applet provided to draw a phase portrait for \( \displaystyle x^\prime = -$c x($a-x)($b-x) \).
$BR
The above equation could represent a model of a population that can 
become extinct if it drops below a particular critical value.  
$BR$BR
What is this critical value?  \{ ans_rule(10) \}
$BR

END_TEXT

# Insert applet

TEXT( MODES(TeX=>'A graph appears here in the html version.', 
  HTML=>$applet->insertAll(debug=>0,includeAnswerBox=>1)));
Context()->normalStrings;

This is the text section of the problem. The TEXT(beginproblem()); line displays a header for the problem, and the Context()->texStrings line sets how formulas are displayed in the text, and we reset this after the text section. Everything between the BEGIN_TEXT and END_TEXT lines (each of which must appear alone on a line) is shown to the student.

Mathematical equations are delimited by \( \) (for inline equations) or \[ \] (for displayed equations); in these contexts inserted text is assumed to be TeX code.

There are a number of variables that set formatting: $BR is a break (like
in HTML). Here, ans_rule(10) is a function that inserts an answer blank 10 characters wide.

############################
#  Answers
############################

$showPartialCorrectAnswers = 1;
Context()->{error}{msg}
  {"'one' is not defined in this context"} = 
  "You have not placed equilibrium points and arrows on the phase line.";
Context()->{error}{msg}
  {"'two' is not defined in this context"} = 
  "You must have an arrow before the first equililbrium point.";
Context()->{error}{msg}
  {"'three' is not defined in this context"} = 
  "You must have an arrow after the last equilibrium point.";
Context()->{error}{msg}
  {"'four' is not defined in this context"} = 
  "Two consecutive arrows must point in the same direction.";
Context()->{error}{msg}
  {"'five' is not defined in this context"} = 
  "There must be an arrow between equilibrium points.";
Context()->{error}{msg}
  {"'six' is not defined in this context"} = 
  "There must be an arrow between an equilibrium point and derivative undefined point.";
Context()->{error}{msg}
  {"'seven' is not defined in this context"} = 
  "There must be an arrow between an equilibrium point and derivative undefined point.";
Context()->{error}{msg}
  {"'eight' is not defined in this context"} = 
  "There must be an arrow between derivative undefined points.";

NAMED_ANS( 'answerBox'=>$anslist->cmp(ordered=>1));
ANS( Compute("$smaller")->cmp());

COMMENT("MathObject version.");

ENDDOCUMENT(); 

This is the answer section of the problem. The problem answer is set by the NAMED_ANS( 'answerBox'=>$anslist->cmp(ordered=>1));, and ANS( Compute("$smaller")->cmp()); lines. The NAMED_ANS line checks the correctness of the student's work using the applet. The applet returns a list. The ordered list answer checker is used to assess correctness.

The solution is embedded in the applet and becomes available when the due date has passed.

The lines that begin Context()->{error}{msg} redefine error messages to messages that are specific to the phasePortrait applet. For example, it makes no sense to have consecutive arrows pointing different directions on a phase portrait so an appropriate error is returned.

The ENDDOCUMENT(); command is the last command in the file.