# PhasePortrait Flash Applet Sample Problem 1

## 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.

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 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
The |

############################# # 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 (
The applet has solution information embedded in it. When
The
The |

################################### # 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
Those portions of the code that begin
the line with You must include the section that
follows |

################################### # 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. |

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 |

############################# # 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
Mathematical equations are delimited by
There are a number of variables that set
formatting: |

############################ # 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 The solution is embedded in the applet and becomes available when the due date has passed. The lines that begin
The |