PhasePortrait Flash Applet Sample Problem 1
Flash Applets embedded in WeBWorK questions phasePortrait Example
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Sample Problem with phasePortrait.swf embedded
This sample problem shows how to use this versatile applet.
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.
A standard WeBWorK PG file with an embedded applet has six sections:
- A tagging and description section, that describes the problem for future users and authors,
- An initialization section, that loads required macros for the problem,
- A problem set-up section that sets variables specific to the problem,
- An Applet link section that inserts the applet and configures it, (this section is not present in WeBWorK problems without an embedded applet)
- A text section, that gives the text that is shown to the student, and
- 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. Because this is a sample problem there isn't a textbook per se, and we've used some default tagging values. 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
The |
TEXT(beginproblem()); ############################# # 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")); |
The phasePortrait.swf applet ...
The applet has solution information embedded in it. When ... |
####################################### # How to use the Graph_Test applet. # Purpose: The purpose of this # applet is to ask graphical # limit questions # Use of applet: The applet # state consists of the # following fields: # qType - question type: limits, # continuity, first_derivative, # second_derivative # hintState - context sensitive # help is either on or off. # Generally turned on after # dueDate # problemSeed - the seed sets # the random parameters that # control which graph is # chosen. If the seed is # 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" |
This is the Applet link section of the problem.
Those portions of the code that begin
the line with |
# # 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"); }, ); |
You must include the section that follows The code |
################################### # Configure applet ################################### # configuration consists of # hintState, question type, and # random seed, and x-coordinates of # four points where jumps, # discontinuities or cusps # occur. $applet->configuration(qq{<xml> <hintState>$hintState</hintState> <qtype>limits</qtype> <seed>$problemSeed</seed> <xlist x1='$x1' x2='$x2' x3='$x3' x4='$x4' /></xml>}); $applet->initialState(qq{<xml> <hintState>$hintState</hintState> <qtype>limits</qtype> <seed>$problemSeed</seed> <xlist x1='$x1' x2='$x2' x3='$x3' x4='$x4' /></xml>}); TEXT( MODES(TeX=>'object code', HTML=>$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"); |
The lines
The hidden form fields are created in the code block:
When the submit button is pressed, the hidden form fields defined in this block are filled with information from the applet. 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. 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. |
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 |
BEGIN_TEXT $BR The graph shown is for the function \(f(x)\). $BR Compute the following quantities: $BR a) \(f($x1)=\) \{ans_rule(35) \} $BR b) \(\lim_{x\to {$x2}^+}f(x)=\) \{ans_rule(35) \} $BR c) \(\lim_{x\to {$x3}^-}f(x)=\) \{ans_rule(35) \} $BR d) \(\lim_{x\to {$x4}}f(x)=\) \{ans_rule(35) \} $BR END_TEXT Context()->normalStrings; |
This is the text section
of the problem. The
Mathematical equations are delimited by
There are a number of variables that set
formatting: |
############################# # # Answers # ## answer evaluators ANS( $correctAnswer1->cmp() ); #checks AnSwEr00001 ANS( $correctAnswer2->cmp() ); #checks AnSwEr00002 ANS( $correctAnswer3->cmp() ); #checks AnSwEr00003 ANS(num_cmp($correctAnswer4, strings=>['DNE'])); #checks AnSwEr00004 ENDDOCUMENT(); |
This is the answer
section of the problem. The problem answer
is set by the The solution is embedded in the applet and becomes available when the due date has passed.
The |