<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.96.4909.6802"?>
<regions>
  <settings>
    <identity>
      <id>be8ed228-7b9f-4d88-9521-f6039e697cd5</id>
      <revision>131</revision>
    </identity>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <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>
    <dependences>
      <assembly name="SMath Studio Desktop" version="0.96.4909.6802" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Math Region" version="0.96.4909.6802" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="Text Region" version="1.9.4909.6785" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="MaximaPlugin" version="1.0.5114.38632" guid="44011c1e-5d0d-4533-8e68-e32b5badce41" />
      <assembly name="Special Functions" version="1.10.4909.6779" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
      <assembly name="Functions' Extension" version="0.0.5093.5251" guid="24c691c1-37f2-49e3-9a84-ccb77304d14a" />
      <assembly name="Plot Region" version="1.8.4909.6768" guid="c451c2b5-798b-4f08-b9ec-b90963d1ddaa" />
      <assembly name="Custom Functions" version="1.0.4902.41872" guid="18dadffd-79a3-4cf9-aee1-d66deb0ea720" />
    </dependences>
  </settings>
  <region id="0" left="18" top="18" width="150" height="33" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <input>
        <e type="operand">ODE</e>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="3">ODE.2</e>
      </input>
    </math>
  </region>
  <region id="1" left="18" top="72" width="126" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Bestandteil des Plugins</p>
    </text>
    <text lang="eng">
      <p>Part of plugin</p>
    </text>
  </region>
  <region id="2" left="243" top="72" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p href="Plugin Maxima.sm">Maxima</p>
    </text>
  </region>
  <region id="3" left="18" top="108" width="490" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Löst gewöhnliche Differenzialgleichungen bis zu zweiter Ordnung.
</p>
    </text>
    <text lang="eng">
      <p>Solves ordinary differential equations up to second order. </p>
    </text>
  </region>
  <region id="4" left="36" top="144" width="37" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">ODE</e>
      </input>
    </math>
  </region>
  <region id="5" left="108" top="144" width="590" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Differentialgleichung. Diese wird so an Maxima übergeben, wie sie ist, 
ohne vorherige Ersetzung von Symbolen.  </p>
    </text>
    <text lang="eng">
      <p>Differential equation, no symbolic substitutions are done prior to the 
call to Maxima. Therefore, the equation must be written verbatim.</p>
    </text>
  </region>
  <region id="6" left="36" top="198" width="40" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
      </input>
    </math>
  </region>
  <region id="7" left="108" top="198" width="144" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Unbekannte Funktion</p>
    </text>
    <text lang="eng">
      <p>unknown function</p>
    </text>
  </region>
  <region id="8" left="36" top="234" width="20" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
      </input>
    </math>
  </region>
  <region id="9" left="108" top="234" width="177" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Unabhängige Variable</p>
    </text>
    <text lang="eng">
      <p>independent variable</p>
    </text>
  </region>
  <region id="10" left="18" top="270" width="660" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Das Ergebnis ist eine boolsche Gleichung, die von Assign() für die Definition der
gesuchten Funktion verwendet werden kann. Die Lösung enthält abhängig von der Ordnung
der DGL eine oder zwei Integrationskonstanten, c (erste Ordnung) oder k1 und k2 bei
zweiter Ordnung.</p>
    </text>
    <text lang="eng">
      <p>The result is a boolean equation which can be used by Assign() for assignment. 
Depending on the order of the ODE, the solution contains one or two integration
constants, named c (first order) or k1 and k2 (second order). </p>
    </text>
  </region>
  <region id="11" left="18" top="342" width="452" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" style="string">cleanup</e>
        <e type="function" preserve="true" args="1">MaximaControl</e>
      </input>
      <result action="symbolic">
        <e type="operand" style="string">Maxima was re-initialized</e>
      </result>
    </math>
  </region>
  <region id="12" left="18" top="378" width="650" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" style="string">all</e>
        <e type="function" preserve="true" args="1">MaximaTakeover</e>
      </input>
      <result action="numeric">
        <e type="operand" style="string">int(), diff(), det(), lim() and sum() now use Maxima</e>
      </result>
    </math>
  </region>
  <region id="13" left="18" top="414" width="292" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Beispiel: freie ungedämpfte Schwingung</p>
    </text>
    <text lang="eng">
      <p underline="true">Example: free undamped oscillation</p>
    </text>
  </region>
  <region id="14" left="36" top="450" width="241" height="37" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">ω</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">0</e>
        <e type="operator" args="2">&gt;</e>
        <e type="function" args="1">assume</e>
        <e type="function" preserve="true" args="1">Maxima</e>
      </input>
      <result action="symbolic">
        <e type="operand">ω</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">0</e>
        <e type="operator" args="2">&gt;</e>
      </result>
    </math>
  </region>
  <region id="15" left="36" top="504" width="564" height="64" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">t</e>
        <e type="function" args="1">w</e>
        <e type="operand">t</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="3">diff</e>
        <e type="operand">ω</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">t</e>
        <e type="function" args="1">w</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">0</e>
        <e type="operator" args="2">≡</e>
        <e type="bracket">(</e>
        <e type="operand">t</e>
        <e type="function" args="1">w</e>
        <e type="operand">t</e>
        <e type="function" preserve="true" args="3">ODE.2</e>
        <e type="function" preserve="true" args="1">Assign</e>
      </input>
      <result action="none">
        <e type="operand">k1</e>
        <e type="operand">ω</e>
        <e type="operand">t</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">*</e>
        <e type="operand">k2</e>
        <e type="operand">ω</e>
        <e type="operand">t</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">sys</e>
      </result>
    </math>
  </region>
  <region id="16" left="234" top="576" width="244" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">t</e>
        <e type="function" args="1">w</e>
      </input>
      <result action="symbolic">
        <e type="operand">k1</e>
        <e type="operand">ω</e>
        <e type="operand">t</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">*</e>
        <e type="operand">k2</e>
        <e type="operand">ω</e>
        <e type="operand">t</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="17" left="18" top="621" width="538" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>Anfangsbedingungen. Mit lim() wird der fehlende at-Operator ersetzt.</p>
    </text>
    <text lang="eng">
      <p>Solve for the integration constants using the initial conditions</p>
    </text>
  </region>
  <region id="18" left="36" top="648" width="354" height="88" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">0</e>
        <e type="function" args="1">w</e>
        <e type="operand">1</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">t</e>
        <e type="function" args="1">w</e>
        <e type="bracket">(</e>
        <e type="operand">t</e>
        <e type="function" preserve="true" args="2">diff</e>
        <e type="operand">t</e>
        <e type="operand">0</e>
        <e type="operator" args="2">≡</e>
        <e type="function" preserve="true" args="2">at</e>
        <e type="operand">1</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>
        <e type="operand">k1</e>
        <e type="operand">k2</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
        <e type="function" preserve="true" args="2">Solve</e>
        <e type="function" preserve="true" args="1">Assign</e>
      </input>
      <result action="none">
        <e type="operand">1</e>
        <e type="operand">ω</e>
        <e type="operator" args="2">/</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">mat</e>
      </result>
    </math>
  </region>
  <region id="19" left="414" top="675" width="232" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">t</e>
        <e type="function" args="1">w</e>
      </input>
      <result action="none">
        <e type="operand">1</e>
        <e type="operand">ω</e>
        <e type="operator" args="2">/</e>
        <e type="operand">ω</e>
        <e type="operand">t</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operand">ω</e>
        <e type="operand">t</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </result>
    </math>
  </region>
  <region id="20" left="36" top="729" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">ω</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="21" left="108" top="729" width="386" height="52" color="#000000" bgColor="#ffffff" fontSize="10">
    <plot type="2d" render="lines" scale_x="0.207900969543163" scale_y="0.226404155832504" scale_z="0.0564036756258981" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-187" transpose_y="2" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">w</e>
      </input>
    </plot>
  </region>
  <region id="22" left="18" top="819" width="283" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p underline="true">Beispiel: freie gedämpfte Schwingung</p>
    </text>
    <text lang="eng">
      <p underline="true">Example: free damped oscillations</p>
    </text>
  </region>
  <region id="23" left="36" top="855" width="146" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">k1</e>
        <e type="operand">k2</e>
        <e type="function" preserve="true" args="2">Clear</e>
      </input>
      <result action="numeric">
        <e type="operand">1</e>
      </result>
    </math>
  </region>
  <region id="24" left="36" top="882" width="322" height="37" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">4</e>
        <e type="operand">k</e>
        <e type="operator" args="2">*</e>
        <e type="operand">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">c</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">-</e>
        <e type="operand">0</e>
        <e type="operator" args="2">&gt;</e>
        <e type="function" args="1">assume</e>
        <e type="function" preserve="true" args="1">Maxima</e>
      </input>
      <result action="none">
        <e type="operand">4</e>
        <e type="operand">k</e>
        <e type="operator" args="2">*</e>
        <e type="operand">m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">c</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">&gt;</e>
      </result>
    </math>
  </region>
  <region id="25" left="369" top="891" width="185" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p>schwache Dämpfung</p>
    </text>
    <text lang="eng">
      <p>undercritical damping</p>
    </text>
  </region>
  <region id="26" left="36" top="927" width="392" height="60" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="0">
      <input>
        <e type="operand">L</e>
        <e type="operand">m</e>
        <e type="operand">t</e>
        <e type="function" args="1">x</e>
        <e type="operand">t</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="3">diff</e>
        <e type="operator" args="2">*</e>
        <e type="operand">c</e>
        <e type="operand">t</e>
        <e type="function" args="1">x</e>
        <e type="operand">t</e>
        <e type="function" preserve="true" args="2">diff</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">k</e>
        <e type="operand">t</e>
        <e type="function" args="1">x</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">0</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">t</e>
        <e type="function" args="1">x</e>
        <e type="operand">t</e>
        <e type="function" preserve="true" args="3">ODE.2</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="27" left="36" top="981" width="603" height="74" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">L</e>
        <e type="function" preserve="true" args="1">Assign</e>
      </input>
      <result action="none">
        <e type="operand">e</e>
        <e type="operand">c</e>
        <e type="operand">t</e>
        <e type="operand">2</e>
        <e type="operand">m</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">k1</e>
        <e type="operand">4</e>
        <e type="operand">k</e>
        <e type="operand">m</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="operand">c</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">m</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">^</e>
        <e type="operand">t</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">*</e>
        <e type="operand">k2</e>
        <e type="operand">4</e>
        <e type="operand">k</e>
        <e type="operand">m</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="operand">c</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">m</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">^</e>
        <e type="operand">t</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="28" left="36" top="1053" width="262" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">m</e>
        <e type="operand">0</e>
        <e type="operator" args="2">&gt;</e>
        <e type="function" args="1">assume</e>
        <e type="function" preserve="true" args="1">Maxima</e>
      </input>
      <result action="symbolic">
        <e type="operand">redundant</e>
      </result>
    </math>
  </region>
  <region id="29" left="36" top="1080" width="427" height="100" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">0</e>
        <e type="function" args="1">x</e>
        <e type="operand">0</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">t</e>
        <e type="function" args="1">x</e>
        <e type="operand">t</e>
        <e type="function" preserve="true" args="2">diff</e>
        <e type="operand">t</e>
        <e type="operand">0</e>
        <e type="operator" args="2">≡</e>
        <e type="function" preserve="true" args="2">at</e>
        <e type="operand">1</e>
        <e type="operator" args="2">≡</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
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    <plot type="2d" render="lines" scale_x="1.91923706299392" scale_y="0.421900912521" scale_z="0.80972786822126" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="-264" transpose_y="1" transpose_z="0">
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      <p href="Plugin Maxima.sm">Maxima</p>
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    <text lang="ger">
      <p href="Function index.sm">Funktionsindex</p>
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    <text lang="eng">
      <p href="Function index.sm">Function index</p>
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    <text lang="ger">
      <p href="Handbook.sm">Inhalt</p>
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    <text lang="eng">
      <p href="Handbook.sm">Contents</p>
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  <region id="41" left="18" top="1683" width="450" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="ger">
      <p italic="true">$Author: mkraska $
$Date: 2013-10-18 17:20:42 +0200 (Fr, 18. Okt 2013) $ </p>
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