<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="11" minor="0"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="false"></View-Properties>
<MapleNet-Properties warnlevel="3" longdelim="true" plotoptions="" echo="1" errorcursor="false" elisiontermsthreshold="10000" elisiontermsbefore="100" errorbreak="1" prettyprint="3" prompt="&gt; " latexwidth="6.0" useclientjvm="true" ansi="false" screenheight="25" labelwidth="20" plotdevice="inline" typesetting="standard" displayprecision="-1" indentamount="4" elisiondigitsthreshold="10000" quiet="false" plotoutput="terminal" rtablesize="10" preplot="" showassumed="1" plotdriver="openviz" elisiontermsafter="100" labelling="true" postplot="" screenwidth="79" elisiondigitsbefore="100" elisiondigitsafter="100" verboseproc="1" imaginaryunit="I" ShowLabels="true"/>
<Styles><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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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 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="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="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="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"/>
<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="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="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="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="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="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="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" 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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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 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 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 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="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="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="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="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="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="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="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="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="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="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="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="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 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="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="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="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"/>
<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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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="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=""/>
<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="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="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="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="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="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=""/>
<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 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<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 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" 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"/>
<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 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 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" 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>
<Page-Numbers enabled="false" first-number="1" first-numbered-page="1" horizontal-location="right" style="Page Number" vertical-location="bottom"/>
<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="L22" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 3.4</Font></Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">To illustrate the process of using the matrizant, consider the initial value problem</Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkmbWZyYWNHRiQ2KC1GIzYlLUkjbW9HRiQ2LVEwJkRpZmZlcmVudGlhbEQ7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjkvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkgtSSNtaUdGJDYlUSJjRicvJSdpdGFsaWNHUSZmYWxzZUYnRjRGNC1GIzYmRjAtRjE2LVEifkYnRjQvRjhGUS9GO0ZRL0Y9RlEvRj9GUS9GQUZRL0ZDRlEvRkVGUUZGRkktRkw2JVEidEYnRk9GNEY0LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zgby8lKWJldmVsbGVkR0ZRRlQtRjE2LVEiPUYnRjRGV0ZYRllGWkZlbkZmbkZnbi9GR1EsMC4yNzc3Nzc4ZW1GJy9GSkZpby1GMTYtUSomdW1pbnVzMDtGJ0Y0RldGWEZZRlpGZW5GZm5GZ24vRkdRLDAuMjIyMjIyMmVtRicvRkpGX3AtRkw2JVEjdGNGJ0ZPRjRGNA==</Equation></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred">                                                                                          (3.15)</Text-field>
<Text-field style="Text" layout="Normal" alignment="centred">c<Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYkLUYjNiQtSSNtbkdGJDYkUSIwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjRGNC1JI21vR0YkNi1RIj1GJ0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRjE2JFEiMUYnRjRGNA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYkLUYjNiQtSSNtbkdGJDYkUSIwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjRGNC1JI21vR0YkNi1RIj1GJ0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRjE2JFEiMUYnRjRGNA==</Equation></Text-field>
<Text-field style="Text" layout="Normal">This equation is solved in Maple by finding the matrizant below.</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, the protected names norm and trace have been redefined and unprotected
</Text-field>
<Text-field style="Warning" layout="Warning">Warning, the name changecoords has been redefined
</Text-field>
</Output>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSJORyIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> Enter the number of terms used in calculating the matrizant.  (Usually 6 terms are sufficient).</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">nvars:=6;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSZudmFyc0ciIic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq:=diff(c(t),t)=-t*c(t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSNFcUcvLSUlZGlmZkc2JC0lImNHNiMlInRHJSJ0RywkKiYlInRHIiIiLSUiY0c2IyUidEciIiIhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=matrix(1,1,[-t]);</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="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(1,1,[1]);</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="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">id:=Matrix(N,N,shape=identity);</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="L11" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"> Define the two dummy variables X1 and X2</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X1:=matrix(N,N);X2:=matrix(N,N);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSNYMUctJSZhcnJheUc2JTsiIiIiIiI7IiIiIiIiNyI=</Equation></Text-field>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSNYMkctJSZhcnJheUc2JTsiIiIiIiI7IiIiIiIiNyI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">A dummy variable t1 is used in the integration.  For matrix integration, Maple's 'map' command should be used.</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X1:=map(int,subs(t=t1,evalm(A)),t1=0..t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUYjNictSSNtaUdGJDYlUSNYMUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjVRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRk4tSShtZmVuY2VkR0YkNiYtRiM2JS1JJ210YWJsZUdGJDY1LUkkbXRyR0YkNiYtSSRtdGRHRiQ2KC1GIzYmLUY4Ni1RKiZ1bWludXMwO0YnRjtGPUZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZfby1GIzYnLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJ0Y7LUZnbzYkUSIyRidGOy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYnAvJSliZXZlbGxlZEdGPy1GODYtUTEmSW52aXNpYmxlVGltZXM7RidGO0Y9RkBGQkZERkZGSEZKL0ZNUSYwLjBlbUYnL0ZQRltxLUYjNiUtSSVtc3VwR0YkNiUtRi42JVEidEYnRjFGNEZqby8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRjtGaHFGO0ZocUY7LyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0Zdci8lK2dyb3VwYWxpZ25HRl1yLyUocm93c3BhbkdGX3AvJStjb2x1bW5zcGFuR0ZfcEZbckZeckZgci8lJmFsaWduR1ElYXhpc0YnL0ZcclEpYmFzZWxpbmVGJy9GX3JGYnAvRmFyUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGMy8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRmJzLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRl10LyUmZnJhbWVHRl10LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGPy8lLWVxdWFsY29sdW1uc0dGPy8lLWRpc3BsYXlzdHlsZUdGPy8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0Zqc0ZocUY7RjsvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGaHFGO0ZocUY7">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat := evalm(id + X1) ;</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="L25" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We now have the first two terms of thematrizant.  The next step is to find the next five terms.  A 'do loop' can be written to find the matrizant:</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 2 to nvars do
S:=evalm( subs(t=t1,evalm(A))&amp;*subs(t=t1,evalm(X1)) ):X2:=
map(int,S,t1=0..t):mat := evalm(mat +X2) :
X1:=evalm(X2):od : evalm(mat) ;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSZJJ1ZlY3Rvckc2IjYjSSdjb2x1bW5HRiU2Iy9JJCVpZEdGJSIqM08mPTo=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=evalm(mat&amp;*Y0);</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="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C:=sol[1,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSJDRywwKiYjIiIiIiIjIiIiKSUidEciIiMiIiIhIiIiIiIiIiIqJiMiIiIiIikiIiIpJSJ0RyIiJSIiIiIiIiomIyIiIiIjWyIiIiokKSUidEciIiciIiIiIiIhIiIqJiMiIiIiJCVRIiIiKSUidEciIikiIiIiIiIqJiMiIiIiJVNRIiIiKiQpJSJ0RyIjNSIiIiIiIiEiIiomIyIiIiImITNZIiIiKSUidEciIzciIiIiIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Thus, the process yields a series solution in t for C.  This solution can be compared to the series solution given by Maple's 'dsolve' command:</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dsolve({Eq,c(0)=1},c(t),type=series);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMvLSUiY0c2IyUidEcrKyUidEciIiIiIiEjISIiIiIjIiIjIyIiIiIiKSIiJS0lIk9HNiMiIiIiIic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">By default, Maple gives a series solution accurate to the order of t<Font superscript="true">6</Font>.  The order of the series solution can be increased by using Maple's order specification as:</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Order:=14;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSZPcmRlckciIzk=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dsolve({Eq,c(0)=1},c(t),type=series);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMvLSUiY0c2IyUidEcrMyUidEciIiIiIiEjISIiIiIjIiIjIyIiIiIiKSIiJSMhIiIiI1siIicjIiIiIiQlUSIiKSMhIiIiJVNRIiM1IyIiIiImITNZIiM3LSUiT0c2IyIiIiIjOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We observe that the series solution obtained using the 'matrizant' method matches exactly with the series solution given by Maple's 'dsolve' command.</Text-field>
</Input>
</Group>
</Worksheet>