﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.98.6179.21440"?>
<regions>
  <settings>
    <identity>
      <id>3b5cba2b-cfbf-4aea-adce-96e84841a25a</id>
      <revision>3</revision>
    </identity>
    <calculation>
      <precision>15</precision>
      <exponentialThreshold>12</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="1" orientation="Portrait" width="850" height="1100" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
    </pageModel>
    <dependencies>
      <assembly name="SMath Studio Desktop" version="0.98.6179.21440" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Math Region" version="0.98.6179.21440" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="Custom Functions" version="1.1.6281.4594" guid="18dadffd-79a3-4cf9-aee1-d66deb0ea720" />
      <assembly name="Special Functions" version="1.11.6179.21442" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
      <assembly name="Text Region" version="1.10.6179.21446" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="X-Y Plot Region (Chart2DLib)" version="0.1.6104.16280" guid="c12231ec-4873-43c1-a7d0-a167ebd17066" />
      <assembly name="Plot Region" version="1.9.6179.21450" guid="c451c2b5-798b-4f08-b9ec-b90963d1ddaa" />
    </dependencies>
    <mode debug="true" />
  </settings>
  <region id="0" left="9" top="36" width="320" height="31" color="#000000" bgColor="#80ffff" fontSize="14">
    <text lang="eng">
      <p bold="true">1. The common conditional. </p>
    </text>
  </region>
  <region id="1" left="18" top="63" width="236" height="62" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">c</e>
        <e type="operand">1</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">x</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">x</e>
        <e type="operand">5</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">4</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operand" style="string" />
        <e type="function" preserve="true" args="3">cases</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="2" left="288" top="72" width="165" height="43" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">u</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operand">x</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operand">x</e>
        <e type="operand">5</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">4</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">≤</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">&amp;</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="3" left="18" top="126" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="6.66022494983235" scale_y="2.85311670611" scale_z="8.86475940822687" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">x</e>
        <e type="function" args="1">c</e>
        <e type="operator" args="2">*</e>
      </input>
    </plot>
  </region>
  <region id="4" left="270" top="126" width="210" height="208" color="#000000" bgColor="#ffffff" fontSize="10">
    <xyplot width="200" height="200" smoothing="false" points="100">
      <propertiessource index="1" sourcetype="PropertyGrid" />
      <grid gridcolor="LightGray" gridpattern="Solid" gridthickness="1" isxgrid="true" isygrid="true" />
      <xaxes xmin="0" xmax="5" xtick="0" numberformat="General" decimalplaces="3" />
      <yaxes ymin="-1" ymax="1" ytick="0.5" numberformat="General" decimalplaces="3" />
      <y2axes isy2axis="false" y2min="-1" y2max="1" y2tick="0.5" numberformat="General" decimalplaces="3" />
      <title2d title="" titlefont="Arial, 12pt" titlefontcolor="Black" />
      <xylabel labelfont="Arial, 10pt" labelfontcolor="Black" tickfont="Courier New, 10pt" tickfontcolor="Black" xlabel="x" ylabel="y" y2label="y2" />
      <legend isbordervisible="true" islegendvisible="false" legendbackcolor="White" legendbordercolor="Black" legendfont="Arial, 8pt" legendposition="NorthEast" textcolor="Black" />
      <traces>
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Blue" linethickness="1" linepattern="Dash" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
      </traces>
      <input>
        <e type="operand">x</e>
        <e type="operand">x</e>
        <e type="function" args="1">u</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
      </input>
    </xyplot>
  </region>
  <region id="5" left="531" top="153" width="116" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">5</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">4</e>
        <e type="operator" args="2">/</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">-</e>
      </input>
      <result action="symbolic">
        <e type="operand">3</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">4</e>
        <e type="operator" args="2">/</e>
      </result>
    </math>
  </region>
  <region id="6" left="531" top="243" width="196" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">5</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">4</e>
        <e type="operator" args="2">/</e>
      </input>
      <result action="numeric">
        <e type="operand">3.92699081698724</e>
      </result>
    </math>
  </region>
  <region id="7" left="9" top="360" width="424" height="31" color="#000000" bgColor="#80ffff" fontSize="14">
    <text lang="eng">
      <p bold="true">2. The 'N-incremented' discretizer. </p>
    </text>
  </region>
  <region id="8" left="459" top="360" width="100" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="9" left="9" top="396" width="325" height="165" border="true" color="#000000" bgColor="#ffffe1" fontSize="10">
    <math decimalPlaces="6">
      <input>
        <e type="operand">#</e>
        <e type="function" args="1">f</e>
        <e type="operand">L</e>
        <e type="operand">Δ</e>
        <e type="operand">N</e>
        <e type="function" args="4">Δinc</e>
        <e type="operand">X</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">N</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">X</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">L</e>
        <e type="operand">Δ</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">X</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">L</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">X</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">vy</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">X</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="1">f</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">X</e>
        <e type="operand">vy</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="10" left="351" top="405" width="193" height="69" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="6">
      <input>
        <e type="operand">L</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
        <e type="operand">Δ</e>
        <e type="operand">3</e>
        <e type="operand">π</e>
        <e type="operator" args="2">*</e>
        <e type="operand">4</e>
        <e type="operand">50</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
        <e type="operand">N</e>
        <e type="operand">50</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="5">mat</e>
        <e type="operand">F</e>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="operand">L</e>
        <e type="operand">Δ</e>
        <e type="operand">N</e>
        <e type="function" args="4">Δinc</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </math>
  </region>
  <region id="11" left="360" top="477" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="7.40024994425817" scale_y="5.05447028499294" scale_z="14.42099361065" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-88" transpose_y="1" transpose_z="0">
      <input>
        <e type="operand">F</e>
      </input>
    </plot>
  </region>
  <region id="12" left="9" top="666" width="228" height="105" border="true" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">#</e>
        <e type="function" args="1">f</e>
        <e type="function" args="1">Q</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">U</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">vx</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">U</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operator" args="2">:</e>
        <e type="operand">vy</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">U</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="1">f</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">vx</e>
        <e type="operand">vy</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="13" left="234" top="666" width="389" height="31" color="#000000" bgColor="#80ffff" fontSize="14">
    <text lang="eng">
      <p bold="true">3. The 'N-in-range' discretizer. </p>
    </text>
  </region>
  <region id="14" left="234" top="702" width="309" height="108" border="true" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math optimize="2" decimalPlaces="4">
      <input>
        <e type="operand">L</e>
        <e type="operand">H</e>
        <e type="operand">N</e>
        <e type="function" args="3">xd</e>
        <e type="operand">U</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">dx</e>
        <e type="operand">H</e>
        <e type="operand">L</e>
        <e type="operator" args="2">-</e>
        <e type="operand">N</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">N</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">U</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">L</e>
        <e type="operand">dx</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operand">dx</e>
        <e type="operand">i</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="1">eval</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">U</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">line</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="15" left="549" top="702" width="157" height="27" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math decimalPlaces="6">
      <input>
        <e type="operand">L</e>
        <e type="operand">5</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">:</e>
        <e type="operand">H</e>
        <e type="operand">5</e>
        <e type="operator" args="2">:</e>
        <e type="operand">N</e>
        <e type="operand">100</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="5">mat</e>
      </input>
    </math>
  </region>
  <region id="16" left="549" top="729" width="119" height="26" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">U</e>
        <e type="operand">L</e>
        <e type="operand">H</e>
        <e type="operand">N</e>
        <e type="function" args="3">xd</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="17" left="549" top="756" width="100" height="50" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="operand">x</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="18" left="648" top="756" width="123" height="35" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="4">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">q</e>
        <e type="operand">0.01</e>
        <e type="operand">x</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="19" left="9" top="810" width="360" height="208" color="#000000" bgColor="#ffffff" fontSize="10" showInputData="False">
    <xyplot width="350" height="200" smoothing="false" points="100">
      <propertiessource index="1" sourcetype="PropertyGrid" />
      <grid gridcolor="LightGray" gridpattern="Solid" gridthickness="1" isxgrid="true" isygrid="true" />
      <xaxes xmin="-8" xmax="8" xtick="2" numberformat="General" decimalplaces="3" />
      <yaxes ymin="-1.25" ymax="1.25" ytick="0.5" numberformat="General" decimalplaces="3" />
      <y2axes isy2axis="false" y2min="-1" y2max="1" y2tick="0.5" numberformat="General" decimalplaces="3" />
      <title2d title="" titlefont="Arial, 12pt" titlefontcolor="Black" />
      <xylabel labelfont="Arial, 10pt" labelfontcolor="Black" tickfont="Courier New, 10pt" tickfontcolor="Black" xlabel="x" ylabel="y" y2label="y2" />
      <legend isbordervisible="true" islegendvisible="false" legendbackcolor="White" legendbordercolor="Black" legendfont="Arial, 8pt" legendposition="NorthEast" textcolor="Black" />
      <traces>
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Blue" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Red" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
      </traces>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="function" args="1">Q</e>
        <e type="operand">x</e>
        <e type="function" args="1">q</e>
        <e type="function" args="1">Q</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </xyplot>
  </region>
  <region id="20" left="369" top="810" width="240" height="158" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="5.55991731349224" scale_y="1.1" scale_z="5.55991731349224" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">F</e>
        <e type="function" args="1">Q</e>
        <e type="operand">x</e>
        <e type="function" args="1">q</e>
        <e type="function" args="1">Q</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </plot>
  </region>
</regions>