Derivatives and Integrals: An Annotated Discourse

<section xml:id="exercises-single" label="section-exercises-single">
  <title>Exercises, One Subsection</title>
  <p>
    This <tag>section</tag> of the sample article demonstrates an
    <q>unstructured division.</q>
    There are no <tag>subsection</tag>,
    you are just reading the first two paragraphs,
    followed by some nonsense text.
    Then there is a <em>single</em>
    <tag>exercises</tag> division.
    Note that this division is not numbered
    (since it is unique within the <tag>section</tag>).
    And a cross-reference to one of the contained <tag>exercise</tag> will be numbered as a member of the <tag>section</tag>,
    <xref ref="exercise-challenging-one-unstructured" text="type-global" />.
  </p>
  <p>
    If you use the unstructured form of a division,
    <em>and</em> have both inline and divisional exercises,
    there is a potential to form ambiguous cross-references.
    To wit, check that <xref ref="duplicate-inline" text="global" /> and <xref ref="duplicate-divisional" text="global" /> are really different exercises
    (which you are <em>unable to do</em>
    if you are reading this in print!).
    The solution is to include the type of exercise in the reference,
    which will assist everybody, but especially your print readers:
    <xref ref="duplicate-inline" text="type-global" /> and <xref ref="duplicate-divisional" text="type-global" />.
  </p>
  <p>
    Compare this section with the similar <xref ref="exercises-multiple" text="type-global" />, next.
    The following text is mostly nonsense,
    just for testing purposes.
  </p>
  <exercise>
    <title>Inline One</title>
    <statement>
      <p>
        Aliquam vitae risus placerat,
        pellentesque leo vitae, iaculis ante.
        Praesent ac odio eget mi bibendum eleifend ac eget metus.
        Morbi in dolor et diam accumsan mattis.
        Aenean elementum pulvinar efficitur.
        Etiam viverra ut tellus quis consequat.
        Phasellus sit amet nisl a ligula pharetra tempus id in elit.
        Maecenas congue quam eu purus fermentum pretium.
        Fusce pellentesque ultricies arcu,
        egestas sollicitudin erat condimentum non.
        Integer non velit at dolor dictum aliquam et rhoncus mauris.
        Sed nec nibh id nunc convallis tincidunt ut at ligula.
        Etiam elementum nisl eu erat dapibus rhoncus.
      </p>
    </statement>
  </exercise>
  <p>
    Pellentesque nec condimentum ligula, quis interdum mauris.
    Ut sed urna lacinia, aliquam arcu id, faucibus nisi.
    Suspendisse potenti.
    Curabitur in erat ultricies, condimentum mi nec, vehicula mauris.
    Duis faucibus risus fermentum velit hendrerit,
    non laoreet massa maximus.
    Donec bibendum elit ac lectus lobortis luctus.
    Ut finibus, dolor ut euismod tristique,
    ligula tortor tempus arcu, finibus semper purus erat ut ligula.
    Aenean accumsan ut ante vel euismod.
  </p>
  <exercise xml:id="duplicate-inline">
    <title>Inline Two</title>
    <p>
      Ut porttitor neque a pharetra euismod.
      Vivamus ut metus pretium, placerat massa tempor, condimentum metus.
      Phasellus vestibulum iaculis turpis non posuere.
      Vestibulum quis aliquet neque.
      Donec nec metus iaculis, laoreet massa vitae, suscipit tellus.
      Etiam et ultrices quam, quis pretium ligula.
      In ut cursus metus.
      Aenean volutpat quam odio, quis tempus dolor egestas eget.
      Nunc fringilla lobortis nunc,
      ut interdum lorem posuere sed.
      Sed sodales risus a laoreet venenatis.
      Nunc sodales tempor mollis.
      Nam sollicitudin velit sed ex viverra feugiat.
      Nunc consectetur mi vitae urna sollicitudin malesuada.
      Fusce eget risus lectus.
      Mauris augue velit,
      vestibulum vitae tempus sit amet, porttitor eget turpis.
    </p>
  </exercise>
  <theorem>
    <title>Major Result</title>
    <p>
      Vivamus tortor tortor, lobortis et sem vel, accumsan placerat libero.
      Sed eget metus non magna accumsan efficitur a non turpis.
      Curabitur maximus arcu ipsum,
      eget vestibulum nulla mollis ac.
      Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas.
      Duis vel eleifend risus.
      Morbi hendrerit tellus eget nibh imperdiet, ac mollis nisl sagittis.
      Ut commodo pharetra leo.
      Suspendisse consequat velit eget velit condimentum feugiat.
    </p>
  </theorem>
  <exercise>
    <title>Inline Three</title>
    <statement>
      <p>
        Suspendisse lacinia mattis risus,
        eget viverra urna dictum eu.
        Maecenas ut sem in turpis egestas varius nec at ipsum.
        Praesent bibendum nisi et turpis congue,
        a pellentesque felis tempor.
        Vivamus non dolor in risus interdum mattis.
        In tempus iaculis velit, sit amet rhoncus tellus aliquam convallis.
        Sed ut tellus id ipsum blandit convallis sed eget tortor.
        Nunc leo felis,
        scelerisque vel ante porta, volutpat rhoncus neque.
        Mauris convallis, felis at aliquam aliquet,
        felis ipsum semper mi, vitae auctor purus ante non erat.
        Ut nec felis mi.
      </p>
    </statement>
  </exercise>
  <exercises xml:id="exercise-collection">
    <title>Exercise Collection</title>
    <exercise>
      <title>Drill One</title>
      <statement>
        <p>
          Lorem ipsum dolor sit amet, consectetur adipiscing elit.
          Cras congue urna nulla.
          Aliquam eget euismod tellus.
          Maecenas nibh libero, venenatis a laoreet in, tempor sit amet sem.
          Morbi sit amet justo tempor velit auctor placerat.
          Maecenas nec lobortis orci.
          Aenean dictum enim lacus, ac blandit lacus elementum nec.
          Mauris porttitor neque volutpat tincidunt sollicitudin.
          Cras porta lectus ac facilisis tempor.
          Suspendisse in velit nisl.
          Sed convallis leo at nunc aliquet fermentum.
          Pellentesque feugiat at ex sed elementum.
          In porta vulputate ipsum sit amet consectetur.
        </p>
        <figure>
          <caption>A figure in an <tag>exercise</tag> in an <em>unstructured</em> division to test that it is numbered as if the containing <tag>exercises</tag> is not present</caption>
          <image xml:id="cross-square-unstructured" width="10%" source="images/cross-square.png" />
        </figure>
        <figure>
          <caption>A side-by-side in a figure in an <tag>exercise</tag> in an <em>unstructured</em> division to test that it is numbered as if the containing <tag>exercises</tag> is not present and to test the numbering of the panels in a solutions manual</caption>
          <sidebyside margins="5%" width="10%">
            <figure>
              <caption>First Panel, subcaptioned</caption>
              <image xml:id="cross-square-unstructured-panel-B1" source="images/cross-square.png" />
            </figure>
            <figure>
              <caption>Second Panel, subcaptioned</caption>
              <image xml:id="cross-square-unstructured-panel-B2" source="images/cross-square.png" />
            </figure>
          </sidebyside>
        </figure>
        <sidebyside margins="5%" width="10%">
          <figure>
            <caption>First Panel, not subcaptioned</caption>
            <image xml:id="cross-square-unstructured-panel-A1" source="images/cross-square.png" />
          </figure>
          <figure>
            <caption>Second Panel, not subcaptioned</caption>
            <image xml:id="cross-square-unstructured-panel-A2" source="images/cross-square.png" />
          </figure>
        </sidebyside>
      </statement>
    </exercise>
    <exercise xml:id="duplicate-divisional">
      <title>Drill Two</title>
      <statement>
        <p>
          Aliquam sagittis ex at magna porttitor,
          quis scelerisque ligula malesuada.
          Vestibulum vitae mauris id nisi pretium ornare a id lectus.
          Nam suscipit magna id sem ultricies vestibulum.
          Nulla facilisi.
          Duis venenatis lectus massa, ac mollis nisi suscipit non.
          Sed et sapien vulputate, imperdiet nibh vel, lobortis nisl.
          Curabitur sagittis justo nibh.
          Nulla vulputate sodales justo at efficitur.
          Cras justo augue, mollis vitae nulla sed,
          vestibulum tincidunt ante.
          Vestibulum et lorem lectus.
          Maecenas accumsan lacus a nisi euismod rutrum eu dapibus justo.
          Etiam scelerisque a odio a euismod.
          Pellentesque vestibulum pellentesque nisi, a tempus erat cursus ac.
          Morbi ut auctor lectus.
        </p>
        <figure>
          <caption>Testing numbering, figure in a <tag>exercise</tag> in an un-numbered <tag>exercises</tag></caption>
          <image source="images/cross-square.png" width="20%" />
        </figure>
      </statement>
    </exercise>
    <exercise>
      <title>Drill Three</title>
      <statement>
        <p>
          Nam congue ex nec justo iaculis maximus.
          Vestibulum lobortis magna sed urna auctor,
          vel dignissim massa posuere.
          In sed venenatis elit.
          Vivamus congue gravida tempus.
          Nunc quis fermentum nisi.
          Nullam hendrerit lorem et tellus semper,
          sit amet scelerisque purus lobortis.
          Quisque sollicitudin quis neque eu suscipit.
          Praesent volutpat justo quis magna vehicula molestie.
        </p>
      </statement>
    </exercise>
    <exercise xml:id="exercise-challenging-one-unstructured">
      <title>Challenging One</title>
      <statement>
        <p>
          Lorem ipsum dolor sit amet, consectetur adipiscing elit.
          Cras congue urna nulla.
          Aliquam eget euismod tellus.
          Maecenas nibh libero, venenatis a laoreet in, tempor sit amet sem.
          Morbi sit amet justo tempor velit auctor placerat.
          Maecenas nec lobortis orci.
          Aenean dictum enim lacus, ac blandit lacus elementum nec.
          Mauris porttitor neque volutpat tincidunt sollicitudin.
          Cras porta lectus ac facilisis tempor.
          Suspendisse in velit nisl.
          Sed convallis leo at nunc aliquet fermentum.
          Pellentesque feugiat at ex sed elementum.
          In porta vulputate ipsum sit amet consectetur.
        </p>
      </statement>
    </exercise>
    <exercisegroup>
      <introduction>
        <p>
          An introduction to an <c>exercisegroup</c>.
          This is here to attempt to interrupt the flow of the counting from this division to the next.
        </p>
      </introduction>
      <exercise>
        <title>Challenging Two</title>
        <statement>
          <p>
            Aliquam sagittis ex at magna porttitor,
            quis scelerisque ligula malesuada.
            Vestibulum vitae mauris id nisi pretium ornare a id lectus.
            Nam suscipit magna id sem ultricies vestibulum.
            Nulla facilisi.
            Duis venenatis lectus massa, ac mollis nisi suscipit non.
            Sed et sapien vulputate, imperdiet nibh vel, lobortis nisl.
            Curabitur sagittis justo nibh.
          </p>
          <p>
            Nulla vulputate sodales justo at efficitur.
            Cras justo augue, mollis vitae nulla sed,
            vestibulum tincidunt ante.
            Vestibulum et lorem lectus.
            Maecenas accumsan lacus a nisi euismod rutrum eu dapibus justo.
            Etiam scelerisque a odio a euismod.
            Pellentesque vestibulum pellentesque nisi, a tempus erat cursus ac.
            Morbi ut auctor lectus.
          </p>
        </statement>
      </exercise>
      <exercise>
        <title>Challenging Three</title>
        <statement>
          <p>
            Nam congue ex nec justo iaculis maximus.
            Vestibulum lobortis magna sed urna auctor,
            vel dignissim massa posuere.
            In sed venenatis elit.
            Vivamus congue gravida tempus.
            Nunc quis fermentum nisi.
            Nullam hendrerit lorem et tellus semper,
            sit amet scelerisque purus lobortis.
            Quisque sollicitudin quis neque eu suscipit.
            Praesent volutpat justo quis magna vehicula molestie.
          </p>
        </statement>
      </exercise>
    </exercisegroup>
    <exercise>
      <title>Impossible One</title>
      <statement>
        <p>
          Lorem ipsum dolor sit amet, consectetur adipiscing elit.
          Cras congue urna nulla.
          Aliquam eget euismod tellus.
          Maecenas nibh libero, venenatis a laoreet in, tempor sit amet sem.
          Morbi sit amet justo tempor velit auctor placerat.
          Maecenas nec lobortis orci.
          Aenean dictum enim lacus, ac blandit lacus elementum nec.
          Mauris porttitor neque volutpat tincidunt sollicitudin.
          Cras porta lectus ac facilisis tempor.
          Suspendisse in velit nisl.
          Sed convallis leo at nunc aliquet fermentum.
          Pellentesque feugiat at ex sed elementum.
          In porta vulputate ipsum sit amet consectetur.
        </p>
      </statement>
    </exercise>
    <exercise>
      <title>Impossible Two</title>
      <statement>
        <p>
          Aliquam sagittis ex at magna porttitor,
          quis scelerisque ligula malesuada.
          Vestibulum vitae mauris id nisi pretium ornare a id lectus.
          Nam suscipit magna id sem ultricies vestibulum.
          Nulla facilisi.
          Duis venenatis lectus massa, ac mollis nisi suscipit non.
          Sed et sapien vulputate, imperdiet nibh vel, lobortis nisl.
          Curabitur sagittis justo nibh.
          Nulla vulputate sodales justo at efficitur.
          Cras justo augue, mollis vitae nulla sed,
          vestibulum tincidunt ante.
          Vestibulum et lorem lectus.
          Maecenas accumsan lacus a nisi euismod rutrum eu dapibus justo.
          Etiam scelerisque a odio a euismod.
          Pellentesque vestibulum pellentesque nisi, a tempus erat cursus ac.
          Morbi ut auctor lectus.
        </p>
      </statement>
    </exercise>
    <exercise>
      <title>Impossible Three</title>
      <statement>
        <p>
          Nam congue ex nec justo iaculis maximus.
          Vestibulum lobortis magna sed urna auctor,
          vel dignissim massa posuere.
          In sed venenatis elit.
          Vivamus congue gravida tempus.
          Nunc quis fermentum nisi.
          Nullam hendrerit lorem et tellus semper,
          sit amet scelerisque purus lobortis.
          Quisque sollicitudin quis neque eu suscipit.
          Praesent volutpat justo quis magna vehicula molestie.
        </p>
      </statement>
    </exercise>
  </exercises>
  <references>
    <title>More Reading</title>
    <introduction>
      <p>
        Left intentionally blank, just checking sectioning.
      </p>
    </introduction>
    <biblio type="raw" xml:id="biblio-lay-article-repeat2">
      David C. Lay,
      <title>Subspaces and Echelon Forms</title>.
      <journal>The College Mathematics Journal</journal>,
      January 1993,
      <volume>24</volume>
      <number>1</number>,
      57<ndash />62.
    </biblio>
  </references>
</section>