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<Text-field style="Title" layout="Title">A Quick Introduction to Maple 11</Text-field>
<Text-field style="Author" layout="Author"><Font bold="true" italic="true">Tim McLarnan</Font></Text-field>
</Input>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font italic="true">Maple</Font> is a tool for doing nearly anything you think of as computational in mathematics, as well as many things you may be surprised to find a machine doing.  Examples include:</Text-field>
<Text-field style="Bullet Item" layout="Bullet Item">Anything you can do with a calculator.</Text-field>
<Text-field style="Bullet Item" layout="Bullet Item">Exact computations with fractions.</Text-field>
<Text-field style="Bullet Item" layout="Bullet Item">Adding, multiplying, and factoring polynomials.</Text-field>
<Text-field style="Bullet Item" layout="Bullet Item">Solving equations, either exactly or approximately.</Text-field>
<Text-field style="Bullet Item" layout="Bullet Item">Simplifying algebraic expressions.</Text-field>
<Text-field style="Bullet Item" layout="Bullet Item">Plotting functions.</Text-field>
<Text-field style="Text" layout="Normal">This leaflet is a quick introduction to some of the salient things <Font italic="true">Maple</Font> can do.  The idea has been to use the most common <Font italic="true">Maple</Font> functions in order to give you examples of their syntax.</Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Five Essential Facts</Text-field></Title>
<Text-field style="List Item" layout="List Item">(1) The <Font italic="true">Maple</Font> prompt is the symbol <Font bold="true">&gt;</Font>.</Text-field>
<Text-field style="List Item" layout="List Item">(2) <Font italic="true">Maple</Font> commands always end with a semicolon ;</Text-field>
<Text-field style="List Item" layout="List Item">(3) <Font italic="true">Maple</Font> commands are always followed by ENTER. If you want to type a command with more than one line, use SHIFT-ENTER to go down a line without executing a command.</Text-field>
<Text-field style="List Item" layout="List Item">(4) <Font italic="true">Maple</Font> is case sensitive.  <Font bold="true">Pi</Font> is not the same as <Font bold="true">pi</Font>.</Text-field>
<Text-field style="List Item" layout="List Item">(5) Save early and often.  <Font italic="true">Maple</Font> seems to crash most often when you are trying to print.  So a recipe for disaster is to do 2 hours of work without ever saving, then try to print.</Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Basic Commands</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font bold="true">+</Font>, <Font bold="true">-</Font>, <Font bold="true">*</Font> and <Font bold="true">/</Font> do what you expect:</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">2+5;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIo</Equation></Text-field>
</Output>
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<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Unlike most calculators, however, <Font italic="true">Maple</Font> does operations with fractions exactly:</Text-field>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IyIkQiMiJFMi</Equation></Text-field>
</Output>
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<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Other arithmetic operations are<Font bold="true">
a^b</Font>, which means <Font italic="true">a</Font> to the power <Font italic="true">b</Font>,<Font bold="true">
n!</Font>, which means <Font italic="true">n</Font> factorial (1*2*3*4*...*<Font italic="true">n</Font>).</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">2^1000;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">ImldbHckcCFvYz9Qb1FDRWxKKUgvbW5AYSdveGs+clgiSDF4ZyVSYWwiZnZ3KVJuNyU+ZSQpXFpZSTojPWF6KD05ckIxMFkyQGEpNEJDW3huWCRSIVtkKXB1dmQlKWZWU0ojcCZHWHI9RG85YHYiSG4lZkYiZWVwOil5JCk+JFxBaCRcN141TnEkKVFdUFcyT2AwPCJbU2gwIj0rZyFcXVVbNEtuaT0yJzM6MiI=</Equation></Text-field>
</Output>
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<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">(355/113)^10;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IyI7RGNeLjYoMyRHIXlbKnlKIjZcW0pBQSoqUW5YUiQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">4!;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiND</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">125!;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">Il14KysrKysrKysrKysrKysrISkzeEpyK2xiUEVWX2JxYWV2WCQpKT15ZiFRVCQ+PjtJMXVkKyRmVzBra0xKI2ZcKilHJEgpbycpKWY4O0xjSk4zOkIpZigpZVUjXHJbT1MmZmQzZyJcLXh3VigqNEUqKSlvPHhFKT0=</Equation></Text-field>
</Output>
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<Text-field style="Text" layout="Normal">Is it  surprise to you that 125! ends in so many zeros?
Can you find a way to compute how many zeros are at the end of <Font italic="true">n</Font>! for any <Font italic="true">n</Font>?<Font bold="true">

Warning:</Font>  Trying anything too huge (like 10000!) may lock up your computer and needlessly antagonize your professor.<Font bold="true">

ifactor(n)</Font> factors the integer <Font italic="true">n</Font> into primes:</Text-field>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ifactor(315);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigtSSFHNiI2IyIiJCIiIy1GJDYjIiImIiIiLUYkNiMiIihGLA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">20! - 12!;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IjQrJVF3cDI/IUhWIw==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">The most recent result (2432902007697638400) can be easily included in any subsequent  calculation without having to type it.  The percent character (<Font bold="true">%</Font>) is used to refer to the last expression computed by <Font italic="true">Maple</Font>.  (The last in time, not necessarily the one just above on the page.)  Similarly, <Font bold="true">%%</Font> is the expression before <Font bold="true">%</Font>, and <Font bold="true">%%%</Font> is the expression before <Font bold="true">%%</Font>.</Text-field>
<Group labelreference="L123" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ifactor(%);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ki4pLUkhRzYiNiMiIiMiIzUiIiIpLUYlNiMiIiQiIiZGKiktRiU2I0YvRihGKi1GJTYjIiIoRiopLUYlNiMiIzZGLkYqLUYlNiMiKT5oKD4lRio=</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">Another way to refer to a previous result<Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> is to use the label number </Font><Font mathcolor="[0,0,0]" mathvariant="italic" mathsize="12" italic="true" fontfamily="Times New Roman" mathbackground="[0,0,0]">Maple</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> places by default after each output line.  Here we factor the 6th number we computed by using </Font><Font mathcolor="[0,0,0]" encoding="UTF-8" mathvariant="bold" mathsize="12" bold="true" fontfamily="Times New Roman" mathbackground="[0,0,0]" fontweight="bold">Insert\342\206\222Label</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> to insert the label (6).  One has to insert labels this way.  One can't just type (6) and have it work.  On the bright side, the labels update automagically if you insert more equations in the middle of a worksheet.</Font></Text-field>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ifactor(<Label label="L9" view="label" executable="true"></Label>);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KmhuLUkhRzYiNiMiIiMiJD4iLUYkNiMiIiQiI2YtRiQ2IyIiJiIjSi1GJDYjIiIoIiM+LUYkNiMiIzYiIzctRiQ2IyIjOCIiKi1GJDYjIiM8RjMtRiQ2I0Y0IiInLUYkNiMiI0JGLy1GJDYjIiNIIiIlLUYkNiNGMEZJLUYkNiMiI1BGKy1GJDYjIiNURistRiQ2IyIjVkYnLUYkNiMiI1pGJy1GJDYjIiNgRictRiQ2I0YsRictRiQ2IyIjaEYnLUYkNiMiI24iIiItRiQ2IyIjckZdby1GJDYjIiN0Rl1vLUYkNiMiI3pGXW8tRiQ2IyIjJClGXW8tRiQ2IyIjKilGXW8tRiQ2IyIjKCpGXW8tRiQ2IyIkLCJGXW8tRiQ2IyIkLiJGXW8tRiQ2IyIkMiJGXW8tRiQ2IyIkNCJGXW8tRiQ2IyIkOCJGXW8=</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Decimal Approximations</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font italic="true">Maple's</Font> normal mode of computation is exact arithmetic, with no roundoff or truncation errors.</Text-field>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">(2^30/3^20)*sqrt(2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJCIiIyMiIiJGJCMiK0M9dXQ1IissV3knWyQ=</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">The function <Font bold="true">evalf()</Font> gives a numerical approximation to this exact expression:</Text-field>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalf(%);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrJT07XU4lISM1</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">If 10 digits aren't enough, give <Font bold="true">evalf</Font> an optional second argument to tell it how many digits you need:</Text-field>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalf(%%,60);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCJnbihSLEYtU15uN1chPjkpXHQhKSoqcE0reUVhKHAoXD07XU4lISNn</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal"><Font italic="true">Maple</Font> uses <Font bold="true">Pi</Font>, not <Font bold="true">pi</Font>, to represent <Equation executable="false" style="2D Math" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=</Equation>.  Notice what this means: variable names in <Font italic="true">Maple</Font> are case-sensitive.
Would you like to know the first few digits of <Equation executable="false" style="2D Math" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=</Equation>?</Text-field>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalf(Pi,200);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCJjdz9RSVwmKltIaVcnZmI1QCZRPnEtVEdddTYiW0ciMyVmYHNKQWVdJjRZJVE0Wm1JI0c4bDNbQCl6MTxATURbLkcnKSoqM2lHMWsieUkjZldcKDQjZTV2JCpScHI+JSlHXXpLUVZFWVFLeiplYEVmVEohJCo+</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal"><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]">Even more surprisingly, </Font><Font italic="true">Maple</Font> can take many decimal numbers and find simple expressions that they might equal.  Here's an example: Suppose I do a calculation and get the result <Equation executable="false" style="2D Math" input-equation="" display="LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEsMi45ODUwMDk4ODlGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUkjbW5HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEsMi45ODUwMDk4ODlGJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn</Equation>.  I may look at that number and not recognize it at all.  <Font mathcolor="[0,0,0]" mathvariant="italic" mathsize="12" italic="true" fontfamily="Times New Roman" mathbackground="[0,0,0]">Maple, </Font>however, does recognize it:</Text-field>
<Group labelreference="L128" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">identify(2.985009889);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJCIiIyMiIiJGJEYmSSNQaUclKnByb3RlY3RlZEdGJQ==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">Knowing that my number is at least close to <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> gives me a useful fact about my number, that perhaps I will then be able to prove.</Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Variable Expressions</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font italic="true">Maple</Font> also works with variables:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">(2*x+7) * (x^2+3) * (x+2)^5;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigsJkkieEc2IiIiIyIiKCIiIkYoLCYqJEYkRiZGKCIiJEYoRigsJkYkRihGJkYoIiIm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">expand(%);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LDQqJEkieEc2IiIiKSIiIyokRiQiIigiI0YqJEYkIiInIiRjIiokRiQiIiYiJEAmKiRGJCIiJSIlcTYqJEYkIiIkIiVXPiokRiRGJyIlJVEjRiQiJXM9IiRzJyIiIg==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">At  this point, <Font italic="true">Maple</Font> has forgotten where it got this polynomial.  It's just a random polynomial of degree 8.  But <Font italic="true">Maple</Font> can factor it:</Text-field>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(%);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigsJkkieEc2IiIiIyIiKCIiIkYoLCYqJEYkRiZGKCIiJEYoRigsJkYkRihGJkYoIiIm</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">Could you have factored this polynomial as fast as <Font italic="true">Maple</Font> did?  Could you have factored it at all?  (If you think about it a bit, your answers to these questions should be &quot;no&quot; and &quot;yes.&quot;)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"><Font italic="true">Maple</Font> doesn't always get the terms of a polynomial in the order you would expect:</Text-field>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">expand((1+x)^3*(x+2)^2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJEkieEc2IiIiIyIjREYkIiM7IiIlIiIiKiRGJCIiJCIjPiokRiRGKSIiKCokRiQiIiZGKg==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">In this case, you can use the <Font bold="true">sort</Font> command to get things arranged.</Text-field>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sort(%);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LC4qJEkieEc2IiIiJiIiIiokRiQiIiUiIigqJEYkIiIkIiM+KiRGJCIiIyIjREYkIiM7RilGJw==</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Assignment and Simplification</Text-field></Title>
<Text-field style="Text" layout="Normal">Often we need to assign a name to the result of a computation.  <Font italic="true">Maple</Font> does this using the syntax<Font bold="true">
variable := value;</Font>
In making an assignment, <Font italic="true">Maple</Font> does some obvious simplifications first.</Text-field>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">e1 := (x+y)^3 * (x+y)^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZTFHNiIqJCksJkkieEdGJCIiIkkieUdGJEYpIiImRik=">KiQsJkkieEc2IiIiIkkieUdGJUYmIiIm</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal"><Font italic="true">Maple</Font> has a built in function called <Font bold="true">simplify</Font>, which tries to simplify expressions.  It does not always find the simplest form of an expression, but it is a start.  Here is an example:</Text-field>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">e2 := (x^3-y^3)/(x^2+x-y-y^2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZTJHNiIqJiwmKiQpSSJ4R0YkIiIkIiIiRisqJClJInlHRiRGKkYrISIiRissKiokKUYpIiIjRitGK0YpRitGLkYvKiQpRi5GM0YrRi9GLw==">KiYsJiokSSJ4RzYiIiIkIiIiKiRJInlHRiZGJyEiIkYoLCoqJEYlIiIjRihGJUYoRipGKyokRipGLkYrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(e2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsKCokSSJ4RzYiIiIjIiIiKiZJInlHRiZGKEYlRihGKCokRipGJ0YoRigsKEYlRihGKEYoRipGKCEiIg==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">To understand what went on here, we can use the commands <Font bold="true">numer</Font> and <Font bold="true">denom</Font> (to take the numerator and denominator of a fraction) together with <Font bold="true">factor</Font>:</Text-field>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(numer(e2));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsJkkieEc2IiIiIkkieUdGJSEiIkYmLCgqJEYkIiIjRiYqJkYnRiZGJEYmRiYqJEYnRitGJkYm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(denom(e2));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsKEkieEc2IiIiIkYmRiZJInlHRiVGJkYmLCZGJEYmRichIiJGJg==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">So what <Font bold="true">simplify</Font> did was to find and remove the common factor of <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZtaW51cztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ5RidGL0YyLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJ0Y5">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZtaW51cztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ5RidGL0YyLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJ0Y5</Equation>.  In this particular case, the commands <Font bold="true">factor</Font> and <Font bold="true">simplify</Font> do the same thing:</Text-field>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">factor(e2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsKCokSSJ4RzYiIiIjIiIiKiZJInlHRiZGKEYlRihGKCokRipGJ0YoRigsKEYlRihGKEYoRipGKCEiIg==</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Solving Equations</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font italic="true">Maple</Font> can also solve equations, even symbolic ones.  Notice the syntax of the commands below.  You have to specify first the equation, then the variables you want to solve for.</Text-field>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(x^2+5*x+2 = 0, x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQsJiMhIiYiIiMiIiIqJCIjPCNGJ0YmRiosJkYkRidGKCMhIiJGJg==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">This quadratic equation had two solutions (separated by a comma), just as you would expect.

If you want a decimal approximation instead of an exact solution to an equation, use <Font bold="true">fsolve</Font> instead of <Font bold="true">solve</Font>.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">fsolve(x^2+5*x+2 = 0, x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQkISs4R2JoWCEiKiQhK3M9WiVRJSEjNQ==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal"><Font bold="true">solve</Font> and <Font bold="true">fsolve</Font> can also deal with systems of more than one equation.  You give them a set of equations (in set brackets <Font bold="true">{ }</Font>) followed by a set of variables to solve for.  Here's an example:</Text-field>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve({x+y=5, x-y=2}, {x,y});</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">PCQvSSJ5RzYiIyIiJCIiIy9JInhHRiUjIiIoRig=</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">Now let's get more adventuresome and try to solve an equation containing symbolic constants:</Text-field>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(a*x^2+b*x+c=0, x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQsJComLCZJImJHNiIiIiIqJCwmKiRGJiIiI0YoKiZJImFHRidGKEkiY0dGJ0YoISIlI0YoRiwhIiJGKEYuRjIjRjJGLCwkKiYsJkYmRihGKUYoRihGLkYyRjM=</Equation></Text-field>
</Output>
</Group>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">Do you recognize this answer?  It's the quadratic formula!</Font></Text-field>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">Did you know that there was a similar formula for solving cubic equations?  It's a bit more complicated:  its output will fill the screen.</Font></Text-field>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(a*x^3 + b*x^2 + c*x + d = 0, x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUYjNistRiM2KS1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYzNiRRIjZGJ0Y2LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZBLyUpYmV2ZWxsZWRHUSZmYWxzZUYnLUkjbW9HRiQ2LVExJkludmlzaWJsZVRpbWVzO0YnRjYvJSZmZW5jZUdGRi8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0Zlbi1GMDYoLUYjNictSSVtc3VwR0YkNiUtSShtZmVuY2VkR0YkNiQtRiM2LS1GIzYtLUYzNiRRIzM2RidGNkZHLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnL0Y3USdpdGFsaWNGJ0ZHLUZqbzYlUSJiRidGXXBGYHBGRy1Gam82JVEiYUYnRl1wRmBwLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSlyZWFkb25seUdGRkY2LUZINi1RKCZtaW51cztGJ0Y2RktGTUZPRlFGU0ZVRlcvRlpRLDAuMjIyMjIyMmVtRicvRmduRmRxLUYjNistRjM2JFEkMTA4RidGNkZHLUZqbzYlUSJkRidGXXBGYHBGRy1GXW82JUZlcC1GMzYkUSIyRidGNi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGaHBGW3FGXnFGNkZgcS1GIzYpLUYzNiRRIjhGJ0Y2RkctRl1vNiVGYnAtRjM2JFEiM0YnRjZGY3JGaHBGW3FGXnFGNi1GSDYtUSIrRidGNkZLRk1GT0ZRRlNGVUZXRmNxRmVxLUYjNi0tRjM2JFEjMTJGJ0Y2RkctSSZtc3FydEdGJDYjRl1zRkctRmlzNiMtRiM2Ly1GIzYrLUYzNiRRIjRGJ0Y2RkdGZXBGRy1GXW82JUZpb0Zdc0ZjckZocEZbcUZecUY2RmBxLUYjNiktRl1vNiVGaW9GYHJGY3JGRy1GXW82JUZicEZgckZjckZocEZbcUZecUY2RmBxLUYjNi8tRjM2JFEjMThGJ0Y2RkdGaW9GR0ZicEZHRmVwRkdGW3JGaHBGW3FGXnFGNkZgcy1GIzYrLUYzNiRRIzI3RidGNkZHLUZdbzYlRltyRmByRmNyRkdGXnJGaHBGW3FGXnFGNkZgcy1GIzYrRmF0RkdGW3JGR0Zbc0ZocEZbcUZecUY2RmhwRltxRl5xRjZGR0ZlcEZocEZbcUZecUY2RmhwRltxRl5xRjZGNi1GIzYpRjItRkg2LVEiL0YnRjZGS0ZNL0ZQRl9wRlFGU0ZVRlcvRlpRLDAuMTY2NjY2N2VtRicvRmduRmF2Rl1zRmhwRltxRl5xRjZGY3JGaHBGW3FGXnFGNi1GIzYnRmVwRmhwRltxRl5xRjZGPEY/RkJGREZocEZbcUZecUY2RmBxLUYjNiktRjA2KEZgckZdc0Y8Rj9GQkZERkctRjA2KC1GIzYnLUYjNiktRiM2K0Zdc0ZHRmVwRkdGaW9GaHBGW3FGXnFGNkZgcS1GIzYnRmp0RmhwRltxRl5xRjZGaHBGW3FGXnFGNkZocEZbcUZecUY2LUYjNilGZXBGR0Zcb0ZocEZbcUZecUY2RjxGP0ZCRkRGaHBGW3FGXnFGNkZgcS1GIzYpLUYwNihGMkZdc0Y8Rj9GQkZERkctRjA2KC1GIzYnRmJwRmhwRltxRl5xRjZGY3ZGPEY/RkJGREZocEZbcUZecUY2RmhwRltxRl5xRjYtRkg2LVEiLEYnRjZGSy9GTkZfcEZPRlFGU0ZVRldGWS9GZ25RLDAuMzMzMzMzM2VtRictRiM2Li1GSDYtUSomdW1pbnVzMDtGJ0Y2RktGTUZPRlFGU0ZVRldGY3FGZXEtRiM2KS1GMDYoRjJGZXNGPEY/RkJGREZHRmhuRmhwRltxRl5xRjZGYHMtRiM2KUZnd0ZHRml2RmhwRltxRl5xRjZGYHFGZXdGYHMtRiM2Ky1GIzYpLUYwNihGMkZgckY8Rj9GQkZERkctRiM2Jy1GMzYkUSJJRidGNkZocEZbcUZecUY2RmhwRltxRl5xRjZGR0Zoc0ZHLUZgbzYkLUYjNilGLUZgc0ZldkZocEZbcUZecUY2RjZGaHBGW3FGXnFGNkZocEZbcUZecUY2Rl14LUYjNi5GZXhGaHhGYHNGXHlGYHFGZXdGYHFGXnlGaHBGW3FGXnFGNkZocEZbcUZecUY2">NiUsKComSSJhRzYiISIiLCoqKEkiY0dGJiIiIkkiYkdGJkYrRiVGKyIjTyomSSJkR0YmRitGJSIiIyEkMyIqJEYsIiIkISIpKihGMyNGK0YwLCwqJkYlRitGKkYzIiIlKiZGKkYwRixGMEYnKipGKkYrRixGK0YlRitGL0YrISM9KiZGL0YwRiVGMCIjRiomRi9GK0YsRjNGOUY2RiVGKyIjNyNGK0YzI0YrIiInKigsJiomRiVGK0YqRitGMyokRixGMEYnRitGJUYnRigjRidGMyMhIiNGMyomRixGK0YlRidGSCwqRiQjRidGQEZERkFGS0ZIKiheI0Y2RitGM0Y2LCZGJEZCRkQjRjBGM0YrRissKkYkRk1GREZBRktGSCooXiMjRidGMEYrRjNGNkZQRitGKw==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">Look at this answer a bit until you undertand the notation.  There are three roots, which are written separated by commas.  The second and third roots also involve <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkmbXNxcnRHRiQ2JC1GIzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk4tSSNtbkdGJDYkUSIxRidGOi8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRidGOi8lK2JhY2tncm91bmRHRldGVUY6RitGVUY6">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JkYrLUkmbXNxcnRHRiQ2JC1GIzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRk4tSSNtbkdGJDYkUSIxRidGOi8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRidGOi8lK2JhY2tncm91bmRHRldGVUY6RitGVUY6</Equation>, which <Font italic="true">Maple</Font> writes as <Font bold="true">I</Font>.<Font bold="true">

Warning again:</Font> <Font bold="true">I</Font> isn't  <Font bold="true">i</Font>.  Case matters to <Font italic="true">Maple</Font>.<Font italic="true">
Maple</Font> can also solve the general fourth degree equation (add in an <Equation executable="false" style="2D Math" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2Iy1JJW1zdXBHRiQ2JS1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiNEYnL0Y7USdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGKw==</Equation> term), though the output now fills several screens.  Can it do more?</Text-field>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(a*x^5 + b*x^4 + c*x^3 + d*x^2 + e*x + f = 0, x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsLiomSSJhR0YnIiIiSSNfWkdGJCIiJkYsKiZJImJHRidGLEYtIiIlRiwqJkkiY0dGJ0YsRi0iIiRGLComSSJkR0YnRixGLSIiI0YsKiZJImVHRidGLEYtRixGLEkiZkdGJ0Ys</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">Why can't <Font italic="true">Maple</Font><Font encoding="UTF-8"> solve this equation?  Because \303\211</Font>variste Galois proved shortly before his death at the age of 20 that there is not general formula like the quadratic formula which solves polynomial equations of degree 5 and higher.  (That is, there is no formula solving all  such equations.  For particular values of the coefficients, there are often simple solutions.)</Text-field>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">fsolve</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> still works to find approximate solutions to equations of high degree, though:</Font></Text-field>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">fsolve(x^5+x+1=0, x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCEraW14W3YhIzU=</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Pagebreak></Pagebreak>
<Text-field style="Heading 1" layout="Heading 1">Plotting Graphs</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font italic="true">Maple</Font> only found one solution to the last equation.  How can we convince ourselves there is only one?  One way to begin to build evidence might be to graph the function.</Text-field>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(x^5+x+1, x=-2..2);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="111" type="two-dimensional" width="156" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">This at least suggests there is only one root between </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">x</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">=2 and </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">x</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">=2.</Font></Text-field>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> sometimes makes an unhelpful choice of axes:</Font></Text-field>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(x^3 - 1/x^2, x=-2..2);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="96" type="two-dimensional" width="176" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">The function has a vertical asymptote. <Font italic="true">Maple's</Font> plot shows <Font italic="true">y</Font> values down to <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGLy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRidGLw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGLy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRidGLw==</Equation>,400,000. You can fix this problem by selecting your own scale for the <Font italic="true">y</Font>-axis:</Text-field>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(x^3 - 1/x^2, x=-2..2, y=-10..10);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="115" type="two-dimensional" width="134" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">There are many options for the </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">plot</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> command, and many other types of plots.
(Try typing </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">?plot[options];</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> or </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">?plots;</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> to learn more about these.)</Font></Text-field>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">Here is an example of a plot of several functions at once.</Font></Text-field>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot({x, x^2, x^3, x^4, x^5}, x=-1.1 .. 1.1);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="140" type="two-dimensional" width="202" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" 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<Text-field style="Text" layout="Normal">One problem with this plot is that you may not be sure which curve is which. To make matters worse, <Font italic="true">Maple</Font> doesn't always assign the same colors to curves: the next time you run it, the colors might change. Here's a way to deal with that: make the functions an ordered list (in square brackets) instead of an unordered set (in curly braces), and give an additional argument listing the colors you want for each curve.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">To plot sin(<Font italic="true">x</Font>) in black, cos(<Font italic="true">x</Font>) in red, and arctan(<Font italic="true">x</Font>) in blue, you could say</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([sin(x),cos(x),arctan(x)], x=-Pi..3*Pi, y=-2..2, color=[black, red, blue]);</Text-field>
</Input>
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<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">If you're color blind or if you're printing in black and white, you can use linestyles instead of colors. Again, <Font bold="true">?plot[options];</Font> will give useful advice.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([sin(x),cos(x),arctan(x)], x=-Pi..3*Pi, y=-2..2, color=black, linestyle=[SOLID, DASH, DOT]);</Text-field>
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</Output>
</Group>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">3D plots are also possible.</Text-field>
<Group labelreference="L41" drawlabel="true">
<Input><Pagebreak></Pagebreak>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(x^2-y^2, x=-2..2, y=-2..2);</Text-field>
</Input>
<Output>
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</Output>
</Group>
<Text-field style="Text" layout="Normal">(To obtain this picture, I ran the <Font italic="true">Maple</Font> command, clicked on the picture, and then played with the choices on the Tool Bar until I got the view I wanted.)  One can also view this 3-dimensional surface as a contour plot.  You can make contour plots from 3D plots using the Tool Bar.</Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Help!</Text-field></Title>
<Text-field style="Text" layout="Normal">In order to use <Font italic="true">Maple</Font> effectively, you'll need to know where to get help.  An excellent and convenient source is <Font italic="true">Maple's</Font> online help, which is available under the Help menu item.  You can also access help directly from the <Font italic="true">Maple</Font> prompt, like this:</Text-field>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">?coeffs;</Text-field>
</Input>
</Group>
<Text-field style="Text" layout="Normal">The output appears in another window, but here it is. It includes a calling sequence, usually some obtuse discussion.  Most usefully, it ends with examples and with suggestions of other related functions to look at.  All functions and libraries which <Font italic="true">Maple</Font> knows about have online help items.  The online help is arranged hierarchically; so if you don't know the name of the command you're looking for, you can often find it by browsing through the help system</Text-field>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2"></Text-field></Title>
<Text-field style="Heading 1" layout="Heading 1">coeffs<Font selection-placeholder="false" executable="false" family="Serif" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" style="Help Normal" font_style_name="Help Normal" size="18"> - extract all coefficients of a multivariate polynomial</Font></Text-field>
<Text-field bookmark="usage" style="Heading 2" layout="Heading 2">Calling Sequence</Text-field>
<Text-field style="Normal" layout="Normal">     coeffs(<Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">p</Font>, <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">x</Font>, <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">'t'</Font>)</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Parameters</Text-field>
<Text-field style="Normal" layout="Normal">     <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Fixed" font_style_name="Help Fixed" size="12">p - </Font>multivariate polynomial</Text-field>
<Text-field style="Normal" layout="Normal">     <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Fixed" font_style_name="Help Fixed" size="12">x - </Font>(optional) indeterminate or list/set of indeterminates</Text-field>
<Text-field style="Normal" layout="Normal">     <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Fixed" font_style_name="Help Fixed" size="12">t - </Font>(optional) an unevaluated name</Text-field>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field bookmark="info" style="Heading 3" layout="Heading 3">Description</Text-field></Title>
<Text-field style="Bullet Item" layout="Bullet Item">The <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">coeffs</Font> function returns an expression sequence of all the coefficients of the polynomial <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">p</Font> with respect to the indeterminate(s) <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">x</Font>. </Text-field>
<Text-field style="Bullet Item" layout="Bullet Item">If <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">x</Font> is not specified, <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">coeffs</Font> computes the coefficients with respect to all the indeterminates of <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">p</Font> (see the <Hyperlink linktarget="Help:indets" hyperlink="true"><Font style="Hyperlink">indets</Font></Hyperlink> function). If a third argument <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">t</Font> is specified (call by name), it is assigned an expression sequence of the terms of <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">p</Font>. There is a one-to-one correspondence between the coefficients and the terms of <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">p</Font>. </Text-field>
<Text-field style="Bullet Item" layout="Bullet Item">Note that <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">p</Font> must be collected (<Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">collect</Font>) with respect to the appropriate indeterminates. For multivariate polynomials, use <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">collect</Font> with <Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" style="Help Maple Name" font_style_name="Help Maple Name" size="12">`distributed`</Font>. </Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field bookmark="examples" style="Heading 3" layout="Heading 3">Examples</Text-field></Title>
<Group labelreference="L119" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">s := 3*v^2*y^2+2*v*y^3;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSJzRywmKigiIiQiIiIpJSJ2RyIiIyIiIiklInlHIiIjIiIiIiIiKigiIiMiIiIlInZHIiIiKSUieUciIiQiIiIiIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L116" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">coeffs( s );</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQiIiQiIiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L118" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">coeffs( s, v, 't' );</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQsJComIiIkIiIiKSUieUciIiNGJkYmLCQqJkYpRiYpRihGJUYmRiY=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L115" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">t;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQqJCklInZHIiIjIiIiRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L117" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p := a*x^2+b*x*y+c*x^2+d*x+e*y+f:
coeffs(collect(p,[x,y],'distributed'),[x,y]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiclImZHJSJiRywmJSJhRyIiIiUiY0dGJyUiZUclImRH</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field bookmark="seealso" style="Heading 3" layout="Heading 3">See Also </Text-field></Title>
<Text-field style="Normal" layout="Normal"><Hyperlink linktarget="Help:collect" hyperlink="true"><Font style="Hyperlink">collect</Font></Hyperlink>, <Hyperlink linktarget="Help:coeff" hyperlink="true"><Font style="Hyperlink">coeff</Font></Hyperlink>, <Hyperlink linktarget="Help:tcoeff" hyperlink="true"><Font style="Hyperlink">tcoeff</Font></Hyperlink>, <Hyperlink linktarget="Help:lcoeff" hyperlink="true"><Font style="Hyperlink">lcoeff</Font></Hyperlink>, <Hyperlink linktarget="Help:indets" hyperlink="true"><Font style="Hyperlink">indets</Font></Hyperlink>, <Hyperlink linktarget="Help:PolynomialTools[CoefficientVector]" hyperlink="true"><Font style="Hyperlink">PolynomialTools[CoefficientVector]</Font></Hyperlink>  </Text-field>
</Section>
</Section>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">The bookshelf in the Math/CS Lounge on the second floor of Dennis contains a fair number of manuals for various versions of <Font italic="true">Maple</Font>. The basics of the program haven't changed much, so any of these manuals should get you started. Other students, faculty, etc. are also good resources. Finally, the <Font italic="true">Maple</Font> Help menu includes, among other things, a couple of pretty complete manuals.</Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Substitutions, Etc.</Text-field></Title>
<Text-field style="Text" layout="Normal">Here are a few more commands which are useful in calculus.  We begin by defining an expression, making some substitutions, and computing its derivative directly from the definition:</Text-field>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">f := x^2+x;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiZkc2IiwmKiQpSSJ4R0YkIiIjIiIiRipGKEYq">LCYqJEkieEc2IiIiIyIiIkYkRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(x=3, f);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiM3</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">subs(x=x+h, f);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJCwmSSJ4RzYiIiIiSSJoR0YmRiciIiNGJ0YlRidGKEYn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">expand(%);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCwqJEkieEc2IiIiIyIiIiomRiRGJ0kiaEdGJUYnRiYqJEYpRiZGJ0YkRidGKUYn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">% - f;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJkkieEc2IiIiIkkiaEdGJUYmIiIjKiRGJ0YoRiZGJ0Ym</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">%/h;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsKComSSJ4RzYiIiIiSSJoR0YmRiciIiMqJEYoRilGJ0YoRidGJ0YoISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(%);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LChJInhHNiIiIiNJImhHRiQiIiJGJ0Yn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">limit(%, h=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCZJInhHNiIiIiMiIiJGJg==</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Defining Functions</Text-field></Title>
<Text-field style="Text" layout="Normal">An irritating feature of this calculation was using <Font bold="true">subs(x=3, f)</Font> to compute <Font italic="true">f</Font> when <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjNGJ0Y5LyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJ0Y5">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjNGJ0Y5LyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJ0Y5</Equation>.  We'd like to be able just to say <Font bold="true">f(3)</Font>, but we can't, because <Font bold="true">f</Font> is just an expression, not a function.  So how would we define a function in <Font italic="true">Maple</Font>?  There are 2 ways.  For simple one-line functions, we can do  this:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">g := x -&gt; x^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiZ0c2ImYqNiNJInhHRiRGJDYkSSlvcGVyYXRvckdGJEkmYXJyb3dHRiRGJCokKUYnIiIjIiIiRiRGJEYk">Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiQ5JCIiI0YlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">This defines <Font italic="true">g</Font> as the function taking <Font italic="true">x</Font> to <Equation executable="false" style="2D Math" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2Iy1JJW1zdXBHRiQ2JS1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiMkYnL0Y7USdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGKw==</Equation>.  We can now use <Font italic="true">g</Font> just like any other function:</Text-field>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">g(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GNlEnbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSlyZWFkb25seUdRJmZhbHNlRidGPA==">KiRJInhHNiIiIiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">g(3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">g(x+h);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiQsJkkieEc2IiIiIkkiaEdGJUYmIiIj</Equation></Text-field>
</Output>
</Group>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">More complicated functions are defined in a more complicated way.  Begin the function with </Font></Text-field>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">proc(</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="true" underline="false" background="[0,0,0]" size="12">variables</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">)</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, and end it with</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12"> end proc;</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">. Here, for instance, is a function which takes 2 arguments, and returns the larger of the two, assuming both are numbers:</Font></Text-field>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h := proc(x,y)
       if x&gt;y
         then x
       else
         y
       end if
     end proc;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiaEc2ImYqNiRJInhHRiRJInlHRiRGJEYkRiRAJTJGKEYnRidGKEYkRiRGJA==">Zio2JEkieEc2IkkieUdGJUYlRiVGJUAlMjklOSRGKkYpRiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h(3,5);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">h(5,3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIm</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">More Calculus Functions</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font italic="true">Maple</Font> can directly compute derivatives, sums, integrals and limits.  Here are some examples:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">diff(sin(x^2),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctRiM2KS1JI21pR0YkNiVRJGNvc0YnLyUnaXRhbGljR0Y4Ri8tRjM2LVEwJkFwcGx5RnVuY3Rpb247RidGL0Y2RjlGO0Y9Rj9GQUZDRkVGSC1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYjNictSSVtc3VwR0YkNiUtRk02JVEieEYnL0ZRUSV0cnVlRicvRjBRJ2l0YWxpY0YnRisvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRicvJSlyZWFkb25seUdGOEYvRmNvRmZvRmlvRi9GL0Zjb0Zmb0Zpb0YvRjJGaW5GY29GZm9GaW9GLw==">LCQqJi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiRJInhHRikiIiMiIiJGLEYuRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">int(x^2, x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJEkieEc2IiIiJCMiIiJGJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">int(x^2, x=1..4);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiNA</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L65" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sum(k^2, k=1..10);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiQmUQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sum(1/k^2, k=1..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJEkjUGlHJSpwcm90ZWN0ZWRHIiIjIyIiIiIiJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y := limit((x^2-3*x+2)/(x-1), x=1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkieUc2IiEiIg==">ISIi</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">Particularly when you are working with second and third derivatives and higher, it is often useful to define a function (rather than an expression) and then to use <Font bold="true">D</Font> to compute a derivative function.  Here's a function and its first, second, and third derivatives, at <Font italic="true">x</Font> and at a numerical point:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">f := x -&gt; x^5+1/x;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiZkc2ImYqNiNJInhHRiRGJDYkSSlvcGVyYXRvckdGJEkmYXJyb3dHRiRGJCwmKiQpRiciIiYiIiJGLyokRichIiJGL0YkRiRGJA==">Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJDkkIiImIiIiKiRGKyEiIkYtRiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">f(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUYjNictSSVtc3VwR0YkNiUtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JFEiNUYnL0Y4USdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lKXJlYWRvbmx5R1EmZmFsc2VGJ0Y+LUkjbW9HRiQ2LVEiK0YnRj4vJSZmZW5jZUdGSy8lKnNlcGFyYXRvckdGSy8lKXN0cmV0Y2h5R0ZLLyUqc3ltbWV0cmljR0ZLLyUobGFyZ2VvcEdGSy8lLm1vdmFibGVsaW1pdHNHRksvJSdhY2NlbnRHRksvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zqbi1JJm1mcmFjR0YkNigtRjs2JFEiMUYnRj4tRiM2J0YwRkNGRkZJRj4vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmpvLyUpYmV2ZWxsZWRHRktGQ0ZGRklGPg==">LCYqJEkieEc2IiIiJiIiIiokRiQhIiJGJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">f(1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L71" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">D(f);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJDkkIiIlIiImKiRGKyEiIyEiIkYlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L72" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">D(f)(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJEkieEc2IiIiJSIiJiokRiQhIiMhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L73" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">D(f)(1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L74" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">(D@@2)(f)(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJEkieEc2IiIiJCIjPyokRiQhIiQiIiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L75" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">(D@@2)(f)(1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiNB</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L76" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">(D@@3)(f)(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJEkieEc2IiIiIyIjZyokRiQhIiUhIic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L77" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">(D@@3)(f)(1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiNh</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Oops!</Text-field></Title>
<Text-field style="Text" layout="Normal">Like any powerful tool, Maple offers any number of ways for you to make mistakes.  Here are some particularly popular ones</Text-field>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Mistake 1: Forgetting you have assigned a value to a variable.:</Text-field></Title>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">Right now, for instance, </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">y</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> has a value: it is </Font><Equation executable="false" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY2LUkjbW9HRiQ2PlEqJnVtaW51czA7RicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvJSdpdGFsaWNHRjcvJSp1bmRlcmxpbmVHRjcvJSpzdWJzY3JpcHRHRjcvJSxzdXBlcnNjcmlwdEdGNy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR0ZCLyUnb3BhcXVlR0Y3LyUrZXhlY3V0YWJsZUdGNy8lKXJlYWRvbmx5R0Y3LyUpY29tcG9zZWRHRjcvJSpjb252ZXJ0ZWRHRjcvJStpbXNlbGVjdGVkR0Y3LyUscGxhY2Vob2xkZXJHRjcvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHRjcvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGYm8tSSNtbkdGJDY1USIxRidGL0YyRjVGOEY6RjxGPkZARkNGRUZHRklGS0ZNRk9GUUZTRlVGL0YyRjVGOEY6RjxGPkZAL0ZEUS5bMjU1LDI1NSwyNTVdRidGRUZHRklGS0ZNRk9GUUZTRlU=</Equation><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">. I'll therefore get into loads of trouble if I try to use </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">y</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> as a variable:</Font></Text-field>
<Group labelreference="L78" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(x^2, x=-1..1, y=-1..2);</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, (in plot) unexpected option: -1 = -1 .. 2</Text-field>
</Output>
</Group>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">To fix this, I need to tell </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> that </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">y</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> is now just the variable </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">y</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> again.  I do that by saying  </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">y:='y';</Font></Text-field>
<Group labelreference="L79" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">ISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L80" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y := 'y';</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkieUc2IkYj">SSJ5RzYi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L81" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">SSJ5RzYi</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Mistake 2: Forgetting a semicolon.</Text-field></Title>
<Text-field style="Text" layout="Normal">If you do this, <Font italic="true">Maple</Font> thinks the expression you want it to evaluate is not over.  The current version of <Font italic="true">Maple,</Font> however, will go ahead and put in the semicolon after a warning:</Text-field>
<Group labelreference="L82" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">2+6</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, inserted missing semicolon at end of statement</Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIp</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Mistake 3: Order of operations.</Text-field></Title>
<Text-field style="Text" layout="Normal"><Font italic="true">Maple</Font> does <Font bold="true">^</Font> first, then <Font bold="true">*</Font> and <Font bold="true">/</Font>, then <Font bold="true">+</Font> and <Font bold="true">-</Font>.  Notice the difference:</Text-field>
<Group labelreference="L83" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">x^1/2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCRJInhHNiIjIiIiIiIj</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">Since <Font italic="true">Maple</Font> does exponentiation before division, it reads this as <Equation executable="false" style="2D Math" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLzYlUSIxRidGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJw==</Equation>/2.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L84" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">x^(1/2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbXNxcnRHRiQ2Iy1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lKXJlYWRvbmx5R1EmZmFsc2VGJy9GNlEnbm9ybWFsRic=">KiRJInhHNiIjIiIiIiIj</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">This is a possible way to write <Equation executable="false" style="2D Math" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkmbXNxcnRHRiQ2Iy1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation>, as is <Font bold="true">sqrt(x)</Font>.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">If you are plotting or solving a complicated expression, it is often useful to get <Font italic="true">Maple</Font> to print it first, so you can be sure you have the parentheses in the right place.  Then either give the expression a name or use copy and paste or use <Font bold="true">%</Font> to get the correct expression into your command.</Text-field>
<Group labelreference="L85" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">-b+sqrt(b^2-4*a*c)/2*a;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCZJImJHNiIhIiIqJiwmKiRGIyIiIyIiIiomSSJhR0YkRipJImNHRiRGKiEiJSNGKkYpRixGKkYv</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">Nuts.  That's not the root of a quadratic.  Let's get the parentheses right.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L86" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">(-b+sqrt(b^2-4*a*c))/(2*a);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJiwmSSJiRzYiISIiKiQsJiokRiUiIiMiIiIqJkkiYUdGJkYsSSJjR0YmRiwhIiUjRixGK0YsRixGLkYnRjE=</Equation></Text-field>
</Output>
</Group>
<Text-field style="Text" layout="Normal">That looks right.  Now I can give it a name and work with it:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L87" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">root1 := %;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkmcm9vdDFHNiIsJCooIyIiIiIiI0YoLCZJImJHRiQhIiIqJCksJiokKUYrRilGKEYoKigiIiVGKEkiYUdGJEYoSSJjR0YkRihGLEYnRihGKEYoRjRGLEYo">LCQqJiwmSSJiRzYiISIiKiQsJiokRiUiIiMiIiIqJkkiYUdGJkYsSSJjR0YmRiwhIiUjRixGK0YsRixGLkYnRjE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L88" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">root2 := (-b-sqrt(b^2-4*a*c))/(2*a);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkmcm9vdDJHNiIsJCooIyIiIiIiI0YoLCZJImJHRiQhIiIqJCksJiokKUYrRilGKEYoKigiIiVGKEkiYUdGJEYoSSJjR0YkRihGLEYnRihGLEYoRjRGLEYo">LCQqJiwmSSJiRzYiISIiKiQsJiokRiUiIiMiIiIqJkkiYUdGJkYsSSJjR0YmRiwhIiUjRixGK0YnRixGLkYnRjE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L89" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">root1*root2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCwmSSJiRzYiISIiKiQsJiokRiUiIiMiIiIqJkkiYUdGJkYsSSJjR0YmRiwhIiUjRixGK0YsRixGLiEiIywmRiVGJ0YoRidGLCNGLCIiJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L90" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(%);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JJW1yb3dHRiQ2Jy1JI21pR0YkNiVRImNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV1GJy8lKXJlYWRvbmx5R1EmZmFsc2VGJy9GNlEnbm9ybWFsRictRiw2Jy1GLzYlUSJhRidGMkY1RjhGO0Y+RkEvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRk0vJSliZXZlbGxlZEdGQA==">KiZJImFHNiIhIiJJImNHRiQiIiI=</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Mistake 4: Leaving out * in Multiplication.</Text-field></Title>
<Text-field style="Text" layout="Normal">I do this all the time.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L91" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">x^2+2x;</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, missing operator or `;`</Text-field>
</Output>
</Group>
<Group labelreference="L92" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(x^2+bx+c=0, x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQqJCwmSSNieEc2IiEiIkkiY0dGJkYnIyIiIiIiIywkRiNGJw==</Equation></Text-field>
</Output>
</Group>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">Here we got the wrong answer because we wrote </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">bx</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, which </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> reads as a new variable, rather than </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">b*x</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, which is what we meant.</Font></Text-field>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"></Text-field>
<Text-field selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[255,255,255]" size="12" linebreak="space" spaceabove="0" rightmargin="0" bullet="none" firstindent="0" bulletsuffix="" linespacing="0.0" pagebreak-before="false" leftmargin="0" alignment="left" initial="0" spacebelow="0"><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">Worst of all, if you write something like </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">2(x)</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">,</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12"> </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> interprets this as a function </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">2</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> evaluated at the point </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">x</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">, and returns just </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="true" italic="false" underline="false" background="[0,0,0]" size="12">2</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12">.  This is obviously not what you intend, and represents a stupid error in the </Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="true" underline="false" background="[0,0,0]" size="12">Maple</Font><Font selection-placeholder="false" executable="false" family="Times New Roman" opaque="false" foreground="[0,0,0]" superscript="false" placeholder="false" readonly="false" subscript="false" bold="false" italic="false" underline="false" background="[0,0,0]" size="12"> parser, but you need to be aware of it.</Font></Text-field>
<Group labelreference="L93" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">1+2(x^2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIk</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Mistake 5: Case sensitivity, or forgetting the name of a command.</Text-field></Title>
<Text-field style="Text" layout="Normal">Here are some examples:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L94" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalf(pi);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">SSNwaUc2Ig==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L95" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalf(Pi);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrYUVmVEohIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L96" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lim(sin(x)/x, x=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUkkbGltRzYiNiQqJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSJ4R0YkIiIiRi0hIiIvRi0iIiE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L97" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">limit(sin(x)/x, x=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIi</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Mistake 6: Notation for trig functions.</Text-field></Title>
<Text-field style="Text" layout="Normal">This is really just a flaw in normal mathematical notation.  When we write <Equation executable="false" style="2D Math" input-equation="">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</Equation>, what we mean is <Equation executable="false" style="2D Math" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2Iy1JJW1zdXBHRiQ2JS1GLDYlUSkoc2luKHgpKUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GO1Enbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRis=</Equation>.  This shorthand is horribly misleading, but it is universal.  Maple is only capable of understanding the second expression, though it will write meaningless strings that may look sensible if you try to use the first expression.</Text-field>
<Group labelreference="L98" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sin^2*x;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiZJJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiI0kieEdGJyIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L99" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalf(sin^2*1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21uR0YkNiRRIjJGJ0Y1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJStiYWNrZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUpcmVhZG9ubHlHRjRGNQ==">KiRJJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IiIiIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L100" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sin(x)^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiQtSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCIiIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L101" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">evalf(sin(1)^2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrJD1NMjMoISM1</Equation></Text-field>
</Output>
</Group>
</Section>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Formatting Text</Text-field></Title>
<Text-field style="Normal" layout="Normal"><Font italic="true">Maple</Font> can be used as a sort of mathematical word-processor, though it's a bit rough.  The basic commands you need to know are:</Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal" layout="Normal">To type text into <Font italic="true">Maple</Font>, hit the little <Font bold="true">T</Font> button near the top of the <Font italic="true">Maple</Font> window, or use <Font encoding="UTF-8" bold="true">Insert\342\206\222Text</Font> or its keyboard shortcut.  This will turn the current group into text instead of a <Font italic="true">Maple</Font> command.</Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal" layout="Normal">To insert a new <Font italic="true">Maple</Font> command or a new block of text, go to <Font encoding="UTF-8" bold="true">Insert\342\206\222Execution Group</Font>, and either insert a new block before or after the one containing the cursor.  There are also keyboard shortcuts for this.</Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal" layout="Normal">To insert superscripts or other mathematical expressions into <Font italic="true">Maple</Font> text, go to <Font encoding="UTF-8" bold="true">Insert\342\206\2222D Math</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> or click </Font><Font mathcolor="[0,0,0]" mathvariant="bold" mathsize="12" bold="true" fontfamily="Times New Roman" mathbackground="[0,0,0]" fontweight="bold">Math</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> in the Toolbar</Font>, then play around with stuff like the Expression palette.  There's lots more about this in the documentation.</Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal" layout="Normal">You can also insert things like paragraphs, sections, and hyperlinks.</Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal" layout="Normal">To use a variable name like <Equation executable="false" style="2D Math" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation>, use <Font bold="true">a[2]</Font>.</Text-field>
<Group labelreference="L102" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">a[0] + a[1]*x + a[2]*x^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgmSSJhRzYiNiMiIiEiIiIqJiZGJDYjRihGKEkieEdGJUYoRigqJiZGJDYjIiIjRihGLEYwRig=</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title><Pagebreak></Pagebreak>
<Text-field style="Heading 1" layout="Heading 1">Other User Interfaces</Text-field></Title>
<Text-field style="Normal" layout="Normal" spaceabove="8" spacebelow="2">It's worth mentioning several other tidbits related to the <Font italic="true">Maple</Font> user interface.</Text-field>
<Text-field style="Normal" layout="Normal" spaceabove="8" spacebelow="2">First, if you have trouble remembering the syntax for common <Font italic="true">Maple</Font> commands, you can click on <Font encoding="UTF-8" bold="true">View\342\206\222Palette\342\206\222Show All</Font> to get a collection of palettes you can click on to insert templates for <Font italic="true">Maple</Font> commands in your worksheet.  By default, these palettes are available to the left side of your <Font italic="true">Maple</Font> window.</Text-field>
<Text-field style="Normal" layout="Normal" spaceabove="8" spacebelow="2">Second, there are several other user interfaces available for <Font mathcolor="[0,0,0]" mathvariant="italic" mathsize="12" italic="true" fontfamily="Times New Roman" mathbackground="[0,0,0]">Maple.</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> This document is a </Font><Font mathcolor="[0,0,0]" mathvariant="italic" mathsize="12" italic="true" fontfamily="Times New Roman" mathbackground="[0,0,0]">Maple</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> worksheet in which the input to each command is formatted as </Font><Font mathcolor="[0,0,0]" mathvariant="italic" mathsize="12" italic="true" fontfamily="Times New Roman" mathbackground="[0,0,0]">Maple</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> input.  This is the stable, old-fashioned way to use </Font><Font mathcolor="[0,0,0]" mathvariant="italic" mathsize="12" italic="true" fontfamily="Times New Roman" mathbackground="[0,0,0]">Maple,</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> and it avoids having to input symbols using the palettes on the left or various keyboard shortcuts.  The cost is that you have to remember the names of a bunch of commands.  You can instead decide to use 2D math notation for input, either by creating a new prompt, clicking on the </Font><Font mathcolor="[0,0,0]" mathvariant="bold" mathsize="12" bold="true" fontfamily="Times New Roman" mathbackground="[0,0,0]" fontweight="bold">Math</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> button in the Toolbar, and then using the palettes to find symbols, or by going to </Font><Font mathcolor="[0,0,0]" encoding="UTF-8" mathvariant="bold" mathsize="12" bold="true" fontfamily="Times New Roman" mathbackground="[0,0,0]" fontweight="bold">Maple 11\342\206\222Preferences\342\206\222Display</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> to set the input display to 2D Math globally.  Here are a couple of examples of how the 2D notation looks:</Font></Text-field>
<Group labelreference="L132" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="int(sin(x), x = 0 .. Pi)" display="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">LUkkaW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtSSRzaW5HRiQ2I0kieEdGJy9GLDsiIiFJI1BpR0Yl</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L133" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="sum(`/`(1, `*`(`^`(n, 2))), n = 1 .. infinity)" display="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">LUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJEkibkdGJyEiIy9GKjsiIiJJKWluZmluaXR5R0Yl</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJEkjUGlHJSpwcm90ZWN0ZWRHIiIjIyIiIiIiJw==</Equation></Text-field>
</Output>
</Group>
<Text-field style="Normal" layout="Normal" spaceabove="8" spacebelow="2">There are also things called not <Font mathcolor="[0,0,0]" mathvariant="italic" mathsize="12" italic="true" fontfamily="Times New Roman" mathbackground="[0,0,0]">Maple</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> worksheets, but </Font><Font mathcolor="[0,0,0]" mathvariant="italic" mathsize="12" italic="true" fontfamily="Times New Roman" mathbackground="[0,0,0]">Maple</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> documents.  Documents are designed to support more extensive word-processing capabilities at the cost of using more keyboard shortcuts and of forcing input to be in 2D form, which means that some of the more advanced options of commands are not available.  To make a </Font><Font mathcolor="[0,0,0]" mathvariant="italic" mathsize="12" italic="true" fontfamily="Times New Roman" mathbackground="[0,0,0]">Maple</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> document, go to </Font><Font mathcolor="[0,0,0]" encoding="UTF-8" mathvariant="bold" mathsize="12" bold="true" fontfamily="Times New Roman" mathbackground="[0,0,0]" fontweight="bold">File\342\206\222New\342\206\222Document Mode</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]">.  If you use </Font><Font mathcolor="[0,0,0]" mathvariant="italic" mathsize="12" italic="true" fontfamily="Times New Roman" mathbackground="[0,0,0]">Maple</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> a lot and want to produce elegant looking documents, you may find documents a good way to go.</Font></Text-field>
<Text-field style="Normal" layout="Normal" spaceabove="8" spacebelow="2">Finally, there is also a command-line version of <Font italic="true">Maple</Font>. You might want this, for instance, if you were connecting to a Linux host via ssh, and you wanted to run <Font italic="true">Maple</Font> without fancy graphics but without the overhead of an X-windows session. To run command-line <Font italic="true">Maple</Font>, type <Font bold="true">maple</Font> at the Linux shell prompt, or <Font bold="true">cmaple</Font> at the Windows command prompt.  On the Mac, assuming a default install, you want to run <Font bold="true">/Library/Frameworks/Maple.framework/Versions/11/bin/maple.</Font> For the record, the ordinary graphical version of <Font italic="true">Maple</Font> is launched under Linux by typing <Font bold="true">xmaple</Font> at the shell prompt.</Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Spreadsheets, Drawings, Etc.</Text-field></Title>
<Text-field style="Text" layout="Normal">Want a spreadsheet in which the cells can contain any <Font italic="true">Maple</Font> expression?  You can <Font encoding="UTF-8" bold="true">Insert\342\206\222Spreadsheet</Font>.  There is more information available from the Help system.  The same thing is true of inserting drawings.  Use <Font mathcolor="[0,0,0]" encoding="UTF-8" mathvariant="bold" mathsize="12" bold="true" fontfamily="Times New Roman" mathbackground="[0,0,0]" fontweight="bold">Insert\342\206\222Image</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> to exist an existing image, or </Font><Font mathcolor="[0,0,0]" encoding="UTF-8" mathvariant="bold" mathsize="12" bold="true" fontfamily="Times New Roman" mathbackground="[0,0,0]" fontweight="bold">Insert\342\206\222Canvas</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[0,0,0]"> to insert a field on which you can draw with basic tools.</Font></Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Packages</Text-field></Title>
<Text-field style="Text" layout="Normal">Many of <Font italic="true">Maple's</Font> commands live in library packages that are not loaded at startup.  You can load one of the packages using the <Font bold="true">with()</Font> command.  Loading a package lists the new functions that have been defined.  Packages can also be loaded and a list of packages can be found by going to <Font encoding="UTF-8" bold="true">Tools\342\206\222Load Package</Font>.  Each package has an associated help file.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L103" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots);</Text-field>
</Input>
<Output>
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</Output>
</Group>
<Group labelreference="L104" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">fieldplot([y,-x], x=-2..2, y=-2..2);</Text-field>
</Input>
<Output>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(Student[Calculus1]);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">RiemannSum(x*(x - 2)*(x - 3), x=0..5, method = upper, output = plot);</Text-field>
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<Text-field style="Text" layout="Normal">Packages you may find yourself wanting include:</Text-field>
<Text-field style="List Item" layout="List Item"><Font bold="true">1. plots</Font>, for all kinds of fancy plots.</Text-field>
<Text-field style="List Item" layout="List Item"><Font bold="true">2. Student[Calculus1]</Font> and various other parts of the <Font bold="true">Student</Font> package, for tools aimed at helping students work with new concepts.</Text-field>
<Text-field style="List Item" layout="List Item"><Font bold="true">3. LinearAlgebra</Font>, for linear algebra, logically enough.  There is also a <Font bold="true">Student[LinearAlgebra]</Font> package.</Text-field>
<Text-field style="List Item" layout="List Item"><Font bold="true">4. DEtools,</Font> for solving and visualizing differential equations.</Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Short Index</Text-field></Title>
<Text-field style="Text" layout="Normal">Is there more to learn about <Font italic="true">Maple</Font>?  Yes!  <Font italic="true">Maple</Font> is a very broad and powerful system for mathematical computation.  It has more than 2000 built-in functions.  The large majority of these have never been used by anyone at Earlham.  Here is a very quick glossary of the most important functions for a calculus student.  More information on all these is available through <Font italic="true">Maple's</Font> online help, or in the written and human sources mentioned above:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" size="10" layout="Normal"><Font family="Monospaced" size="10">+, -, *, /         Add, subtract, multiply, divide.
^                  Raise a number to a power.
!                  Factorial.
-&gt;                 Used in procedure definitions.
=                  Used in inputting equations.
:=                 Used to assign a value to a variable.
&lt;, &gt;, &lt;=, &gt;=, &lt;&gt;   Mean &lt;, &gt;, , , and , resp.
%, %%, %%%         Previous expressions.
..                 An interval.
[ ]                List. Lists are ordered.
{ }                Set. Sets are unordered.
abs                Computes the absolute value of a number.
coeff              Get one coefficient of a polynomial.
collect            Collect coefficients of like powers.
combine            Combine terms into a single term.
convert            Convert from one data type to another.
cos                Cosine. Arguments are in radians.
D                  Differential operator.
denom              Denominator.
diff               Differentiate.
exp(1)             e, The base for natural logs.
evalf              Evaluate an expression as a decimal approximation.
exp                Exponential function.  exp(x) = E^x.
expand             Expand out an expression.
factor             Factor a polynomial.
for...do...end do  Repeat commands.
fsolve             Find approximate solutions to one or more equations.
help               Get help on a function.
if...then...else...end if    Conditionals.
ifactor            Factor an integer.
int                Integrate a function.
Int                Write down the integral, but don't evaluate. Use with changevar.
IntTutor           Student[Calculus1] command to explore ways to evaluate an integral.
limit              Compute limits.
Limit              Write doen but don't evaluate a limit.
ln, log            Compute natural logs.  ln(x)=log(x)log10(x).
max                Compute the maximum of 2 or more numbers.
min                Compute the minimum of 2 or more numbers.
normal             Put a fraction in normal form.  A useful special case of simplify.
numer              Numerator.
op                 Pick out one part of an expression.
plot               Plot a graph.
plot3d             Plot a 3D graph.
print              Pretty-print an expression.
proc               Define a procedure.
product            Product of finitely or infinitely many terms.
quo                Quotient of 2 polynomials.
rem                Remainder of 2 polynomials.
simplify           Try to simplify an expression.
sin                Sine.  The arguments to trig functions should be in radians.
solve              Solve 1 or more equations exactly.
sort               Sort a list or the terms in a polynomial.
sqrt               Square root.
Student            A set of tutorial packages.  Student[Calculus1] is one of these.
sum                Sum of finitely or infinitely many terms.
Sum                Sum written down, but not worked out.
Taylor             Taylor series expansion.
value              evaluate a Sum, Limit, or Int.
with               Load a library package.  Example: with(plots);</Font></Text-field>
</Section>
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