# PhasePortrait Flash Applet Sample Problem 1

## 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.  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
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();

"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";

$anslist = List("sink",Compute("0"),"source",Compute("$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
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.