<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="12" minor="2"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="false"></View-Properties>
<MapleNet-Properties elisiondigitsbefore="100" labelling="true" indentamount="4" elisiontermsthreshold="10000" ansi="false" errorbreak="1" useclientjvm="true" echo="1" imaginaryunit="I" labelwidth="20" plotdriver="openviz" elisiondigitsafter="100" plotoutput="terminal" rtablesize="10" elisiontermsbefore="100" elisiondigitsthreshold="10000" typesetting="standard" plotdevice="inline" verboseproc="1" showassumed="1" errorcursor="false" longdelim="true" plotoptions="" quiet="false" elisiontermsafter="100" screenwidth="79" preplot="" prettyprint="3" displayprecision="-1" warnlevel="3" screenheight="25" latexwidth="6.0" postplot="" prompt="&gt; " ShowLabels="true"/>
<Styles><Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 3" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 5" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Maple Name" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[104,64,92]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Bold" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Italic" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Menus" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Fixed Width" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal256" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Plot Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="8" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Nonterminal" background="[255,255,255]" bold="true" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Heading" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Italic" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Variable" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Italic Bold" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Default" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Underlined Italic" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Dash Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,255]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Bold Small" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="1" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Small" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="1" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Page Number" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Output Labels" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="8" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Bullet Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Plot Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Emphasized" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Symbol 2" background="[255,255,255]" bold="false" executable="false" family="SymbolPi" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Comment" background="[255,255,255]" bold="true" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Author" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input Placeholder" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[200,0,200]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="true"/>
<Font name="Code" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Plot" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="9" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[64,128,64]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Inert Output" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[144,144,144]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Italic Small" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="1" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Comment" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Underlined Bold" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Copyright" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,128,128]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Help Underlined" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Prompt" background="[255,255,255]" bold="true" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Input" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Header and Footer" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Error" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 1" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Bold" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Notes" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 4" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Equation Label" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="LaTeX" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 3" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 2" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Popup" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,128,128]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Dictionary Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[147,0,15]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Left Justified Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="List Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Fixed" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Layout name="Ordered List 1" alignment="left" bullet="numeric" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 3" alignment="left" bullet="roman" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 5" alignment="left" bullet="ROMAN" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Annotation Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Fixed Width" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Normal256" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Help" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Diagnostic" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Normal" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.5" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="4" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Bullet Item" alignment="left" bullet="dot" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 4" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 3" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="2" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Left Justified Maple Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.5" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="List Item" alignment="left" bullet="indent" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Pencil-style name="Pencil 5" pen-color="[255,0,0]" pen-height="5.0" pen-width="5.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
</Styles>
<Footer left-content="" center-content="" right-content="&amp;[Page]" left-image-scale-width="100" center-image-scale-width="100" right-image-scale-width="100" left-image-scale-height="100" center-image-scale-height="100" right-image-scale-height="100" date-format="2" selected-index="0" first-number="1" first-numbered-page="1"/>
<Task-table>
    <Task-category name="&lt;default&gt;">
    </Task-category>
</Task-table>
<Annotation-table>
    <Annotation-category name="&lt;default&gt;">
    </Annotation-category>
</Annotation-table>
<Task>
</Task>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Example 8.7 Heat Conduction with an Insulator Boundary Condition</Text-field>
<Text-field style="Text" layout="Normal">Example (8.1.17) is solved in Maple below:</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">First, the governing equations and boundary conditions are converted to the Laplace domain and solved in the Laplace domain:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eq:=diff(u(x,t),t)=diff(u(x,t),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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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLC1GJDYkLUYkNiRGJ0YrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">u(x,0):=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=diff(u(x,t),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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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGKyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(x,t)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JInVHNiI2JEkieEdGJUkidEdGJSIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqs:=laplace(eq,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqs:=subs(laplace(u(x,t),t,s)=U(x),eqs);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LyomSSJzRzYiIiIiLUkiVUdGJTYjSSJ4R0YlRiYtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYsNiRGJ0YqRio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc1:=laplace(bc1,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(laplace(u(x,t),t,s)=U(x),bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJVRzYiNiNJInhHRilGKyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc2:=laplace(bc2,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(laplace(u(x,t),t,s)=U(x),bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkYmMyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYnLUYjNictRiw2JVEiVUYnRi9GMi1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GWi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInhGJ0YvRjIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRjlGOUZeb0Y5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJ0Y5LUYjNiUtRiw2JVEic0YnRi9GMkZeb0Y5LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZlcC8lKWJldmVsbGVkR0Y9Rl5vRjlGXm9GOQ==">Ly1JIlVHNiI2I0kieEdGJSokSSJzR0YlISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dsolve(eqs,U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlVHNiI2I0kieEdGJSwmKiZJJF9DMUdGJSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKiYpSSJzR0YlI0YrIiIjRitGJ0YrRitGKyomSSRfQzJHRiVGKy1GLTYjLCRGMiEiIkYrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=c[1]*cosh(s^(1/2)*x)+c[2]*sinh(s^(1/2)*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJiZJImNHNiI2IyIiIkYoLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjKiYpSSJzR0YmI0YoIiIjRihJInhHRiZGKEYoRigqJiZGJTYjRjNGKC1JJXNpbmhHRitGLkYoRig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq0:=eval(subs(x=0,bc1));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LyomJkkiY0c2IjYjIiIjIiIiKUkic0dGJiNGKUYoRikiIiE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq1:=eval(subs(x=1,bc2));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LywmKiYmSSJjRzYiNiMiIiJGKS1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRic2IyokKUkic0dGJyNGKSIiI0YpRilGKSomJkYmNiNGNEYpLUklc2luaEdGLEYvRilGKSokRjIhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">con:=solve({eq0,eq1},{c[1],c[2]});</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCQvJkkiY0c2IjYjIiIiKiYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMqJClJInNHRiYjRigiIiNGKCEiIkYyRjUvJkYlNiNGNCIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution obtained in the Laplace domain is:</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=subs(con,U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJClJInNHRigjIiIiIiIjRi4hIiJGLEYwLUYkNiMqJkYrRi5JInhHRihGLkYu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The polynomials are:<Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P(s):=numer(U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYpSSJzR0YnIyIiIiIiI0YtSSJ4R0YnRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q(s):=denom(U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJClJInNHRigjIiIiIiIjRi5GLkYsRi4=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Note that the order of q(s) is greater than the order of p(s).</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A(s):=P(s)/diff(Q(s),s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJilJInNHRigjIiIiIiIjRi5JInhHRihGLkYuLCYqKEYtRi4tSSVzaW5oR0YlNiMqJEYrRi5GLkYrRi5GLi1GJEY1Ri4hIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The roots of Q(s) are found as:</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(Q(s),s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQsJComIyIiIiIiJUYmKUkjUGlHJSpwcm90ZWN0ZWRHIiIjRiYhIiIiIiE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">_EnvAllSolutions := true;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVExX0VudkFsbFNvbHV0aW9uc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JUYxRi9GMi8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGOQ==">SSV0cnVlRyUqcHJvdGVjdGVkRw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(Q(s),s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQsJCooIyIiIiIiJUYmKUkjUGlHJSpwcm90ZWN0ZWRHIiIjRiYpLCZGJkYmKiZGK0YmSSVfWjF8aXJHNiJGJkYmRitGJiEiIiIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The roots can be taken as:</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">0,-((2*n-1)*Pi/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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">NiQiIiEsJCooIyIiIiIiJUYnKSwmKiYiIiNGJ0kibkc2IkYnRidGJyEiIkYsRicpSSNQaUclKnByb3RlY3RlZEdGLEYnRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, the coefficients are found:</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(s=mu,A(s)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCIiIyIiIi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomKUkjbXVHRisjRiVGJEYlSSJ4R0YrRiVGJSwmKiYtSSVzaW5oR0YoNiMqJEYuRiVGJUYuRiVGJSomRiRGJS1GJ0Y2RiVGJSEiIkYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">First A0 is found:</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[0]:=subs(mu=0,A[n]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGPi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEjOj1GJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZMLyUpc3RyZXRjaHlHRkwvJSpzeW1tZXRyaWNHRkwvJShsYXJnZW9wR0ZMLyUubW92YWJsZWxpbWl0c0dGTC8lJ2FjY2VudEdGTC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmVuLUY7NiRRIjFGJ0Y+RkBGPg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The coefficient An for values n = 1..\342\210\236 can be found as:</Font></Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(mu^(1/2)=I*(2*n-1)/2*Pi,A[n]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCIiJSIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqKiNGJSIiI0YlLCYqJkYwRiVJIm5HRitGJUYlRiUhIiJGJUkjUGlHRilGJUkieEdGK0YlRiVGJSwoKipGMEYlLUkkc2luR0YoNiMsJCooRi9GJUYxRiVGNUYlRiVGJUY1RiVGM0YlRiUqJkY5RiVGNUYlRjQqJkYkRiUtRidGO0YlRjRGNEY0</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">A<Font subscript="true">n</Font> is simplified as:</Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:={cos(1/2*(2*n-1)*Pi)=0,sin(1/2*(2*n-1)*Pi)=(-1)^(n-1)};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEldmFyc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtZmVuY2VkR0YkNiYtRiM2Jy1GIzYnLUYjNictRiw2JVEkY29zRicvRjBGPUY5LUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZqbi1GUDYkLUYjNiUtRiM2Jy1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGOS1GZm82JFEiMkYnRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmFwLyUpYmV2ZWxsZWRHRj0tRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjlGO0Y+RkBGQkZERkZGSEZpbkZbby1GIzYmLUZQNiQtRiM2Ji1GIzYmRmlvRmZwLUYsNiVRIm5GJ0YvRjJGOS1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmhxRmVvRjlGOUZmcC1GLDYlUScmIzk2MDtGJ0ZlbkY5RjkvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRjlGXXJGOUY5Rl1yRjktRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRmZvNiRRIjBGJ0Y5Rl1yRjktRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZpbi9GTlEsMC4zMzMzMzMzZW1GJy1GIzYnLUYjNictRiw2JVEkc2luRidGZW5GOUZmbkZcb0ZdckY5RmByLUklbXN1cEdGJDYlLUZQNiQtRiM2JS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkhGZ3FGaXFGZW9GOUY5LUYjNiZGYXFGZHFGZW9GOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGXXJGOUZdckY5RjkvJSVvcGVuR1EifGZyRicvJSZjbG9zZUdRInxockYnRl1yRjk=">PCQvLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJCooIyIiIiIiI0YuLCYqJkYvRi5JIm5HRilGLkYuRi4hIiJGLkkjUGlHRidGLkYuIiIhLy1JJHNpbkdGJkYqKUYzLCZGMkYuRi5GMw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(vars,A[n]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqLCIiJSIiIikhIiIsJEkibkc2IkYnRiUtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRio2IywkKiojRiUiIiNGJSwmKiZGNEYlRilGJUYlRiVGJ0YlSSNQaUdGLkYlSSJ4R0YqRiVGJUYlRjdGJ0Y1RidGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The general terms in the Laplace domain solution are (see equation (8.1.16)):</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u0s:=A[0]*1/s;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiRJInNHNiIhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The inverse Laplace transform is:</Text-field>
</Input>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u0t:=invlaplace(u0s,s,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkdTB0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y5">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The term in the infinite series is</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">uns:=A[n]/(s-mu);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqLiIiJSIiIikhIiIsJEkibkc2IkYnRiUtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRio2IywkKiojRiUiIiNGJSwmKiZGNEYlRilGJUYlRiVGJ0YlSSNQaUdGLkYlSSJ4R0YqRiVGJUYlRjdGJ0Y1RicsJkkic0dGKkYlSSNtdUdGKkYnRidGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">unt:=invlaplace(uns,s,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqLiIiJSIiIikhIiIsJEkibkc2IkYnRiUtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRio2IywkKiojRiUiIiNGJSwmKiZGNEYlRilGJUYlRiVGJ0YlSSNQaUdGLkYlSSJ4R0YqRiVGJUYlRjdGJ0Y1RictSSRleHBHRi02IyomSSNtdUdGKkYlSSJ0R0YqRiVGJUYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">unt:=subs(mu=-((2*n-1)/2*Pi)^2,unt);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqLiIiJSIiIikhIiIsJEkibkc2IkYnRiUtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRio2IywkKiojRiUiIiNGJSwmKiZGNEYlRilGJUYlRiVGJ0YlSSNQaUdGLkYlSSJ4R0YqRiVGJUYlRjdGJ0Y1RictSSRleHBHRi02IywkKiojRiVGJEYlKUY1RjRGJSlGN0Y0RiVJInRHRipGJUYnRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The final solution is obtained as:</Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U:=u0t+Sum(unt,n=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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">LCYiIiJGIy1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLCQqLiIiJUYjKSEiIiwkSSJuR0YpRi9GIy1JJGNvc0dGJjYjLCQqKiNGIyIiI0YjLCYqJkY4RiNGMUYjRiNGI0YvRiNJI1BpR0YnRiNJInhHRilGI0YjRiNGO0YvRjlGLy1JJGV4cEdGJjYjLCQqKiNGI0YtRiMpRjlGOEYjKUY7RjhGI0kidEdGKUYjRi9GI0YjL0YxO0YjSSlpbmZpbml0eUdGJ0Yj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">As in chapter 7, the initial condition is used at time, t = 0, to avoid Gibb\342\200\231s phenomenon:</Font></Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=piecewise(t=0,0,t&gt;0,subs(infinity=20,U));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The following plots are obtained:</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(u,x=0..1,t=0..1,axes=boxed,title=&quot;Figure Exp. 8.13.&quot;,labels=[x,t,&quot;u&quot;],orientation=[-150,60]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 13692 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([subs(t=0,u),subs(t=0.1,u),subs(t=0.2,u),subs(t=0.3,u)],x=0..1,axes=boxed,title=&quot;Figure Exp. 8.14.&quot;,thickness=5,labels=[x,&quot;u&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">[encoded data, 9052 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group>
</Worksheet>