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> |
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</p> |
</p> |
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+ | <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> |
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<p> |
<p> |
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− | 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 |
+ | 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> |
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+ | The first image shows the homework problem unstarted. The second image shows the homework problem successfully completed. |
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<br> |
<br> |
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[[File:phasePortraitprob11_1.jpg]] |
[[File:phasePortraitprob11_1.jpg]] |
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Line 90: | Line 91: | ||
All of the tagging information exists to |
All of the tagging information exists to |
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allow the problem to be easily indexed. |
allow the problem to be easily indexed. |
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− | Because this is a sample problem there |
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+ | There is an on-line |
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− | isn't a textbook per se, and we've used |
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− | some default tagging values. There is an on-line |
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[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 |
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[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')). |
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Line 98: | Line 97: | ||
|- style=" background-color:#ddffdd;" |
|- style=" background-color:#ddffdd;" |
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| <pre> |
| <pre> |
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− | DOCUMENT(); |
+ | DOCUMENT(); |
loadMacros( |
loadMacros( |
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− | + | "PGstandard.pl", |
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− | + | "MathObjects.pl", |
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− | + | "AppletObjects.pl", |
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); |
); |
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</pre> |
</pre> |
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Line 114: | Line 113: | ||
|- style=" background-color:#ffffdd;" |
|- style=" background-color:#ffffdd;" |
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| <pre> |
| <pre> |
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− | # Set up problem |
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+ | ############################# |
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− | $qtype='limits'; |
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+ | # Setup |
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+ | ############################# |
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− | $showHint = 0; |
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+ | Context("Numeric"); |
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+ | Context()->flags->set( |
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+ | tolerance => 0.1, |
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+ | tolType => "absolute", |
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+ | ); |
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+ | |||
+ | $a=random(1,4,1); |
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+ | $b=random(1,4,1); |
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+ | if($b==$a){ |
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+ | $b++; |
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+ | } |
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+ | $varLabel = "x"; |
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+ | $smaller = $b; |
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+ | $bigger = $a; |
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+ | if($a<$b){ |
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+ | $smaller = $a; |
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+ | $bigger = $b; |
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+ | } |
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+ | |||
+ | $c=random(2,5,1); |
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+ | |||
+ | $xmin = Compute("-$bigger-2"); |
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+ | $xmax = Compute("$bigger+2"); |
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+ | |||
+ | $showSolution = false; |
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if(time>$dueDate){ |
if(time>$dueDate){ |
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− | $showHint=1; |
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+ | $showSolution=true; |
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} |
} |
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− | $x1=random(-8,-2,1); |
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+ | $arrow1 = Compute("($xmin)/2"); |
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− | $x2=$x1+random(2,4,1); |
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+ | $arrow2 = Compute("($smaller)/2"); |
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− | $x3=$x2+random(2,3,1); |
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+ | $arrow3 = Compute("($smaller+$bigger)/2"); |
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− | $x4=random($x3+2,7,1); |
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+ | $arrow4 = Compute("($xmax+$bigger)/2"); |
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+ | $arrow1dir = "r"; |
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+ | $arrow2dir = "l"; |
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+ | $arrow3dir = "r"; |
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+ | $arrow4dir = "l"; |
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+ | |||
+ | Context()->strings->add(sink=>{},source=>{},node=>{},inc=>{},dec=>{},all=>{},usource=>{},usink=>{}); |
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+ | $anslist = List("sink",Compute("0"),"source",Compute("$smaller"),"sink",Compute("$bigger")); |
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</pre> |
</pre> |
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| <p> |
| <p> |
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− | The GraphLimits.swf applet will accept four different question types, specified with the <code>$qtype</code> variable. These are: limits, continuity, first_derivative and second_derivative. This sample problem is set to 'limits'. |
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+ | 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>$varLabel = "x";</code> sets the function to x. When the student moves the mouse along the phase line 'x=[mouse location]' is displayed. We also set the minimum and maximum values of the phase line. |
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</p> |
</p> |
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<p> |
<p> |
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− | The applet has solution |
+ | The applet has solution information embedded in it. When <code>$solutionState=false</code>, this information is not shown. When <code>$solutionState=true</code>, this information is revealed. The <code>time</code> parameter tracks the current date and time. The conditional compares that to the due date for the problem set (in the <code>$dueDate</code> scalar variable) and sets <code>$solutionState</code> to true if the due date has passed and leaves <code>$solutionState</code> set to false if the assignment is not yet due. |
</p> |
</p> |
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<p> |
<p> |
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− | The four variables <code>$x1</code>, <code>$x2</code>, <code>$x3</code> and <code>$x4</code> are the x-coordinates of four points on the graph that the applet will set to be a removable discontinuity, a jump discontinuity or a cusp. The order of these phenomena is random as are the y-values chosen. The x-coordinates must be between -10 and 10. |
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+ | The <code>$arrow</code> variables are used by the applet when <code>$solutionState</code> is true to display the correct placement of the arrows. |
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+ | </p> |
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+ | <p> |
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+ | 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. |
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</p> |
</p> |
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|- style=" background-color:#ccffff;" |
|- style=" background-color:#ccffff;" |
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| <pre> |
| <pre> |
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− | + | ################################### |
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− | # |
+ | # Create link to applet |
− | # |
+ | ################################### |
− | + | $appletName = "phasePortrait"; |
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− | + | $applet = FlashApplet( |
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− | + | codebase => findAppletCodebase("$appletName.swf"), |
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− | + | appletName => $appletName, |
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− | + | appletId => $appletName, |
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− | + | setStateAlias => 'setXML', |
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− | + | getStateAlias => 'getXML', |
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− | + | setConfigAlias => 'setConfig', |
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− | + | maxInitializationAttempts => 5, # number of attempts to initialize applet |
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− | + | answerBoxAlias => 'answerBox', |
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− | + | height => '400', |
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− | + | width => '550', |
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− | + | bgcolor => '#e8e8e8', |
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− | + | debugMode => 0, |
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− | + | submitActionScript => |
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− | + | qq{getQE("answerBox").value=getApplet("$appletName").getAnswer() }, |
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− | + | ); |
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− | # changed. |
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− | ####################################### |
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− | # qType = limits |
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− | # right_limits - returns a |
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− | # list of points (a,b) |
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− | # such that |
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− | # lim_{x\to a^-}f(x)=b, |
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− | # but |
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− | # lim_{x\to a^+}f(x)\= b |
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− | # left_limits - returns a |
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− | # list of points (a,b) |
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− | # such that |
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− | # lim_{x\to a^+}f(x)=b, |
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− | # but |
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− | # lim_{x\to a^-}f(x)\= b |
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− | # neither_limits - returns |
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− | # a list of points (a,b) |
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− | # such that |
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− | # lim_{x\to a^-}f(x)\= |
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− | # lim_{x\to a^+}f(x)\= |
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− | # f(a)=b |
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− | # get_intervals returns a |
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− | # list of intervals on |
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− | # which f(x) is continuous. |
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− | # get_f_of_x - given x value, |
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− | # returns f(x). |
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− | # returns NaN for x notin |
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− | # [-10,10]. |
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− | # getf_list - given x value |
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− | # and string returns |
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− | # "function" - returns f(x) |
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− | # "leftlimit" - returns |
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− | # lim_{x->a^-}f(x) |
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− | # "rightlimit" - returns |
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− | # lim_{x->a^+}f(x) |
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− | # "limit" - returns |
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− | # lim_{x->a}f(x) or "DNE" |
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</pre> |
</pre> |
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− | | <p>This is the <strong>Applet link section</strong> of the problem. |
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+ | | <p> |
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− | </p><br> |
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+ | This is the <strong>Applet link section</strong> of the problem. |
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+ | </p> |
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+ | <br> |
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<p> |
<p> |
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Those portions of the code that begin |
Those portions of the code that begin |
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Line 168: | Line 204: | ||
to your particular problem. |
to your particular problem. |
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</p> |
</p> |
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− | |- style=" background-color:#ccffff;" |
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+ | <p>You must include the section that |
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− | | <pre> |
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− | # |
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− | # What does the applet do? |
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− | # The applet draws a graph |
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− | # with jumps, a cusp and |
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− | # discontinuities |
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− | # When turned on, there is |
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− | # context sensitive help. |
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− | ################################ |
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− | ############################ |
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− | # Create link to applet |
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− | ############################ |
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− | $appletName = "Graph_Limit"; |
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− | $applet = FlashApplet( |
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− | codebase |
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− | => findAppletCodebase |
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− | ("$appletName.swf"), |
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− | appletName |
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− | => $appletName, |
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− | appletId |
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− | => $appletName, |
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− | setStateAlias |
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− | => 'setXML', |
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− | getStateAlias |
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− | => 'getXML', |
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− | setConfigAlias |
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− | => 'setConfig', |
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− | maxInitializationAttempts |
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− | => 10, |
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− | height |
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− | => '475', |
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− | width |
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− | => '425', |
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− | bgcolor |
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− | => '#e8e8e8', |
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− | debugMode |
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− | => 0, |
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− | submitActionScript |
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− | => qq{ |
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− | getQE("func").value=getApplet |
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− | ("$appletName").getf_list($x1,"function"); |
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− | getQE("rlimit").value=getApplet |
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− | ("$appletName").getf_list($x2,"rightlimit"); |
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− | getQE("llimit").value=getApplet |
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− | ("$appletName").getf_list($x3,"leftlimit"); |
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− | getQE("limit").value=getApplet |
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− | ("$appletName").getf_list($x4,"limit"); |
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− | }, |
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− | ); |
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− | </pre> |
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− | | <p>You must include the section that |
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follows <code># Create link to |
follows <code># Create link to |
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applet</code>. If you are embedding |
applet</code>. If you are embedding |
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− | a different applet, from the |
+ | a different applet, from the phasePortrait |
applet, put your applet name in place of |
applet, put your applet name in place of |
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− | ' |
+ | 'phasePortrait' in the line <code>$appletName =</code> |
− | <code> " |
+ | <code> "phasePortrait";</code>. |
Enter the height of the applet |
Enter the height of the applet |
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− | in the line <code>height => ' |
+ | in the line <code>height => '400',</code> |
− | in place of |
+ | in place of 400 and the width in the line |
− | <code>width => ' |
+ | <code>width => '550',</code> in place of 550. |
</p><br> |
</p><br> |
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− | <p>The code <code>qq{ </code><code> |
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− | getQE("func").value=getApplet</code> |
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− | <code>("$appletName").getf_list($x1,"function");</code><code> |
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− | getQE("rlimit").value=getApplet</code> |
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− | <code>("$appletName").getf_list($x2,"rightlimit");</code><code> |
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− | getQE("llimit").value=getApplet</code> |
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− | <code>("$appletName").getf_list($x3,"leftlimit");</code><code> |
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− | getQE("limit").value=getApplet</code> |
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− | <code>("$appletName").getf_list($x4,"limit");</code><code> |
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− | }</code> |
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− | is called when the 'Submit Answers' |
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− | button in the problem is pressed. |
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− | There is an external interface function |
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− | designed inside the applet. The function |
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− | name is 'getf_list'. These lines of code |
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− | call the function with javascript. |
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− | <code>getf_list</code>, takes two arguments: |
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− | the x-coordinate of a point, and a string |
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− | value. The string may be any of the |
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− | following four alternatives: "function", |
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− | "rightlimit", "leftlimit", "limit". |
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− | <code>getf_list</code> returns either |
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− | the value of the function at the x-coordinate, |
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− | or the specified limit. The line <code> |
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− | getQE("func").value=getApplet</code> |
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− | <code>("$appletName").getf_list($x1,"function");</code> |
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− | gets the value of the function at <code>$x1</code> |
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− | and stores this value in the hidden javascript |
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− | form field named "func".</p> |
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|- style=" background-color:#ccffff;" |
|- style=" background-color:#ccffff;" |
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| <pre> |
| <pre> |
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Line 266: | Line 222: | ||
# Configure applet |
# Configure applet |
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################################### |
################################### |
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− | # configuration consists of |
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+ | $config_string = <<"ENDCONFIG"; |
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− | # hintState, question type, and |
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+ | <XML> |
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− | # random seed, and x-coordinates of |
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+ | <leng>400</leng> |
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− | # four points where jumps, |
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+ | <vari>$varLabel</vari> |
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− | # discontinuities or cusps |
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+ | <xmin>$xmin</xmin> |
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− | # occur. |
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+ | <xmax>$xmax</xmax> |
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− | $applet->configuration(qq{<xml> |
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+ | <showSolution>$showSolution</showSolution> |
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− | <hintState>$hintState</hintState> |
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+ | <solutionPts> |
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− | <qtype>limits</qtype> |
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+ | <aPicon lrn='$arrow1dir' loc='$arrow1'></aPicon> |
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− | <seed>$problemSeed</seed> |
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+ | <aPicon lrn='n' loc='0'></aPicon> |
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− | <xlist x1='$x1' x2='$x2' |
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+ | <aPicon lrn='$arrow2dir' loc='$arrow2'></aPicon> |
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− | x3='$x3' x4='$x4' /></xml>}); |
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+ | <aPicon lrn='n' loc='$smaller'></aPicon> |
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− | $applet->initialState(qq{<xml> |
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+ | <aPicon lrn='$arrow3dir' loc='$arrow3'></aPicon> |
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− | <hintState>$hintState</hintState> |
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+ | <aPicon lrn='n' loc='$bigger'></aPicon> |
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− | <qtype>limits</qtype> |
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+ | <aPicon lrn='$arrow4dir' loc='$arrow4'></aPicon> |
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− | <seed>$problemSeed</seed> |
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+ | </solutionPts> |
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− | <xlist x1='$x1' x2='$x2' |
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+ | </XML> |
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− | x3='$x3' x4='$x4' /></xml>}); |
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+ | ENDCONFIG |
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− | |||
− | TEXT( MODES(TeX=>'object code', |
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− | HTML=>$applet->insertAll( |
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− | debug=>0, |
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− | includeAnswerBox=>0, |
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− | ))); |
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− | |||
− | TEXT(MODES(TeX=>"", HTML=><<'END_TEXT')); |
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− | <input type="hidden" |
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− | name="func" id="func" /> |
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− | <input type="hidden" |
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− | name="llimit" id="llimit" /> |
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− | <input type="hidden" |
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− | name="rlimit" id="rlimit" /> |
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− | <input type="hidden" |
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− | name="limit" id="limit" /> |
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− | END_TEXT |
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− | |||
− | $answerString1 = |
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− | $inputs_ref->{func}; |
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− | my $correctAnswer1 = |
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− | Compute("$answerString1"); |
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− | |||
− | $answerString2 = |
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− | $inputs_ref->{rlimit}; |
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− | my $correctAnswer2 = |
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− | Compute("$answerString2"); |
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− | |||
− | $answerString3 = |
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− | $inputs_ref->{llimit}; |
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− | my $correctAnswer3 = |
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− | Compute("$answerString3"); |
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− | |||
− | $answerString4 = |
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− | $inputs_ref->{limit}; |
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− | my $correctAnswer4 = |
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− | Compute("$answerString4"); |
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+ | $applet->configuration($config_string); |
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+ | $applet->initialState($config_string); |
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</pre> |
</pre> |
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− | | <p> The lines <code>$applet->configuration</code> |
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+ | | <p> This configuration information is sent to the applet to set it up. <code>leng</code> sets the length in pixels of the phase line. <code>vari</code> sets the variable name. The default is y; we have set it to x here. We set the minimum and maximum values of the phase line. The defaults are -10 and 10. The default for <code>showSolution</code> is false. We set it to true when the <code>dueDate</code> has passed. <code>solutionPts</code> values are only used if <code>showSolution</code> is true. <code>aPicon</code> are tokens that will be placed on the phase line when the due date is past. <code>lrn</code> takes four possible values: 'l' for left arrow, 'r' for right arrow, 'n' for node or equilibrium point, and 'u' for undefined value of the derivative. <code>loc</code> provides the location of the token on the phase line. |
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− | <code>(qq{<xml><hintState>$hintState</hintState></code> |
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− | <code><qtype>$qtype</qtype></code> |
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− | <code><seed>$problemSeed</seed></code> |
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− | <code><xlist x1='$x1' x2='$x2'</code> |
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− | <code> x3='$x3' x4='$x4' /></code> |
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− | <code></xml>});</code> and <code>$applet</code> |
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− | <code>->initialState</code><code>(qq{<xml></code> |
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− | <code><hintState>$hintState</hintState></code> |
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− | <code><qtype>$qtype</qtype></code><code><seed>$problemSeed</seed></code> |
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− | <code><xlist x1='$x1' x2='$x2'</code><code> x3='$x3' x4='$x4' /></code> |
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− | <code></xml>});</code> configure the applet. |
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− | The configuration of the applet is done in xml. |
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− | The hintState is set to the variable |
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− | <code>$hintState</code>, the question type is set to |
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− | <code>$qtype</code> and the problem seed is the |
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− | WeBWorK environmental variable <code>$problemSeed</code>. |
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− | The variables <code>$x1</code>, <code>$x2</code>, |
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− | <code>$x3</code> and <code>$x4</code> are also |
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− | passed to the applet. |
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− | </p><br> |
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− | <p> |
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− | The hidden form fields are created in the code block: |
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− | <code> |
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− | TEXT(MODES(TeX=>"", HTML=><<'END_TEXT')); |
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− | <input type="hidden"</code> |
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− | <code> name="func" id="func" /></code> |
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− | <code> |
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− | <input type="hidden"</code> |
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− | <code> name="llimit" id="llimit" /></code> |
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− | <code> |
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− | <input type="hidden"</code> |
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− | <code> name="rlimit" id="rlimit" /></code> |
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− | <code> |
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− | <input type="hidden"</code> |
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− | <code> name="limit" id="limit" /></code> |
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− | <code> |
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− | END_TEXT |
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− | </code> |
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− | The line <code>TEXT(MODES(TeX=>"", HTML=><<'END_TEXT'));</code> |
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− | prevents the hidden fields from becoming part of the hard copy. |
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− | </p><br> |
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− | |||
− | <p> |
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− | <code>TEXT( MODES(TeX=>'object code',</code> |
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− | <code> HTML=>$applet->insertAll(</code> |
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− | <code> |
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− | debug=>0,</code> |
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− | <code> |
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− | includeAnswerBox=>0,</code> |
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− | <code> |
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− | reinitialize_button=>$permissionLevel>=10,</code> |
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− | <code> |
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− | )));</code> actually embeds the applet |
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− | in the WeBWorK problem. |
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− | </p><br> |
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− | <p>When the submit button is pressed, the |
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− | hidden form fields defined in this block are |
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− | filled with information from the applet. |
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</p> |
</p> |
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− | <p> |
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− | The data from the hidden form fields is used |
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− | in these simple perl subroutines to define the |
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− | correct answers to the four questions that are |
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− | part of this WeBWorK problem.</p> |
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− | <p>The WeBWorK variable $answerString1 is the |
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− | content of the hidden form field "func". |
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− | $correctAnswer1 is the solution to the first |
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− | question. The solutions for the next two |
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− | questions are defined in a similar way. |
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− | The final question also has 'DNE' as a possible |
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− | correct answer for the student to enter. The |
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− | way that the applet is designed, the left and |
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− | right limits always exist.</p> |
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|- style=" background-color:#ccffff;" |
|- style=" background-color:#ccffff;" |
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| <pre> |
| <pre> |
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Line 416: | Line 265: | ||
|- style=" background-color:#ffdddd;" |
|- style=" background-color:#ffdddd;" |
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| <pre> |
| <pre> |
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+ | ############################# |
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+ | # Main text |
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+ | ############################# |
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+ | TEXT(beginproblem()); |
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+ | |||
+ | Context()->texStrings; |
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BEGIN_TEXT |
BEGIN_TEXT |
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− | |||
+ | Use the applet provided to draw a phase portrait for \( \displaystyle x^\prime = -$c x($a-x)($b-x) \). |
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$BR |
$BR |
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− | The graph shown is for the |
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+ | The above equation could represent a model of a population that can |
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− | function \(f(x)\). |
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+ | become extinct if it drops below a particular critical value. |
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− | $BR Compute the following |
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+ | $BR$BR |
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− | quantities: |
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+ | What is this critical value? \{ ans_rule(10) \} |
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$BR |
$BR |
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− | a) |
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− | \(f($x1)=\) |
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− | \{ans_rule(35) \} |
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− | $BR |
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− | b) |
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− | \(\lim_{x\to {$x2}^+}f(x)=\) |
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− | \{ans_rule(35) \} |
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− | $BR |
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+ | END_TEXT |
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− | c) |
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− | \(\lim_{x\to {$x3}^-}f(x)=\) |
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− | \{ans_rule(35) \} |
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− | $BR |
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+ | # Insert applet |
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− | d) |
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− | \(\lim_{x\to {$x4}}f(x)=\) |
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− | \{ans_rule(35) \} |
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− | $BR |
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+ | TEXT( MODES(TeX=>'A graph appears here in the html version.', |
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− | END_TEXT |
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+ | HTML=>$applet->insertAll(debug=>0,includeAnswerBox=>1))); |
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Context()->normalStrings; |
Context()->normalStrings; |
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</pre> |
</pre> |
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Line 468: | Line 310: | ||
<p> |
<p> |
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There are a number of variables that set |
There are a number of variables that set |
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− | formatting: <code>$ |
+ | formatting: <code>$BR</code> is a break (like <code><BR></code> in HTML). Here, <code>ans_rule(10)</code> |
− | + | is a function that inserts an answer blank 10 |
|
− | [[FormatVariableList|This page]] gives a list |
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− | of variables like this. Finally, <code>\{ \}</code> |
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− | sets off <em>code that will be executed |
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− | in the problem text</em>. Here, <code>ans_rule(35)</code> |
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− | is a function that inserts an answer blank 35 |
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characters wide. |
characters wide. |
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</p> |
</p> |
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|- style=" background-color:#eeccff;" |
|- style=" background-color:#eeccff;" |
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| <pre> |
| <pre> |
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− | + | ############################ |
|
− | # |
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# Answers |
# Answers |
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− | # |
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+ | ############################ |
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− | ## answer evaluators |
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− | ANS( $correctAnswer1->cmp() ); |
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+ | $showPartialCorrectAnswers = 1; |
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− | #checks AnSwEr00001 |
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+ | Context()->{error}{msg} |
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− | ANS( $correctAnswer2->cmp() ); |
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+ | {"'one' is not defined in this context"} = |
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− | #checks AnSwEr00002 |
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+ | "You have not placed equilibrium points and arrows on the phase line."; |
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− | ANS( $correctAnswer3->cmp() ); |
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+ | Context()->{error}{msg} |
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− | #checks AnSwEr00003 |
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+ | {"'two' is not defined in this context"} = |
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− | ANS(num_cmp($correctAnswer4, |
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+ | "You must have an arrow before the first equililbrium point."; |
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− | strings=>['DNE'])); |
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+ | Context()->{error}{msg} |
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− | #checks AnSwEr00004 |
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+ | {"'three' is not defined in this context"} = |
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+ | "You must have an arrow after the last equilibrium point."; |
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+ | Context()->{error}{msg} |
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+ | {"'four' is not defined in this context"} = |
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+ | "Two consecutive arrows must point in the same direction."; |
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+ | Context()->{error}{msg} |
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+ | {"'five' is not defined in this context"} = |
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+ | "There must be an arrow between equilibrium points."; |
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+ | Context()->{error}{msg} |
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+ | {"'six' is not defined in this context"} = |
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+ | "There must be an arrow between an equilibrium point and derivative undefined point."; |
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+ | Context()->{error}{msg} |
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+ | {"'seven' is not defined in this context"} = |
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+ | "There must be an arrow between an equilibrium point and derivative undefined point."; |
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+ | Context()->{error}{msg} |
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+ | {"'eight' is not defined in this context"} = |
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+ | "There must be an arrow between derivative undefined points."; |
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+ | NAMED_ANS( 'answerBox'=>$anslist->cmp(ordered=>1)); |
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+ | ANS( Compute("$smaller")->cmp()); |
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− | ENDDOCUMENT(); |
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+ | COMMENT("MathObject version."); |
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+ | |||
+ | 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> |
+ | is set by the <code>NAMED_ANS( 'answerBox'=>$anslist->cmp(ordered=>1));</code>, and |
− | <code>ANS( $ |
+ | <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( $correctAnswer3->cmp() );</code>, |
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− | and <code>ANS(num_cmp</code> |
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− | <code>($correctAnswer4,</code> |
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− | <code>strings=>['DNE']));</code> lines. |
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− | These compare the student's answer with the |
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− | answers returned from the applet. Answers 1-3 |
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− | follow the same basic structure. The fourth |
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− | answer allows for either a numeric answer or |
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− | the string 'DNE' for limits that do not exist. |
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</p> |
</p> |
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<p> |
<p> |
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Line 502: | Line 363: | ||
becomes available when the due date has passed. |
becomes available when the due date has passed. |
||
</p> |
</p> |
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+ | <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> |
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<p> |
<p> |
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The <code>ENDDOCUMENT();</code> command is the |
The <code>ENDDOCUMENT();</code> command is the |
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Line 507: | Line 369: | ||
</p> |
</p> |
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|} |
|} |
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+ | |||
+ | |||
+ | [[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.
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. 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 |
############################# # 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 Applet link section of the problem.
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 text section
of the problem. 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 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 lines that begin
The |