<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE document PUBLIC "-//CNX//DTD CNXML 0.5 plus MathML//EN" "http://cnx.rice.edu/technology/cnxml/schema/dtd/0.5/cnxml_mathml.dtd">
<document xmlns="http://cnx.rice.edu/cnxml" xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:bib="http://bibtexml.sf.net/" xmlns:m="http://www.w3.org/1998/Math/MathML" id="new">
  <name>MathML Examples</name>
  <metadata>
  <md:version>1.2</md:version>
  <md:created>2007/09/28 11:56:21 GMT-5</md:created>
  <md:revised>2007/09/28 12:34:39.826 GMT-5</md:revised>
  <md:authorlist>
      <md:author id="hungtran">
      <md:firstname>Tran</md:firstname>
      <md:othername>Viet</md:othername>
      <md:surname>Hung</md:surname>
      <md:email>hungtran@vef.gov</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="hungtran">
      <md:firstname>Tran</md:firstname>
      <md:othername>Viet</md:othername>
      <md:surname>Hung</md:surname>
      <md:email>hungtran@vef.gov</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>MathML Example</md:keyword>
  </md:keywordlist>

  <md:abstract>This is to demonstrate math content in Vietnam OpenCourseWare. The math content is collected from Connexions project at http://cnx.org.</md:abstract>
</metadata>
  <content>
    <equation id="element-576"><name>Example 1:</name>
<m:math display="block">
	    <m:apply>
	      <m:eq/>
	      <m:apply>
		<m:plus/>
		<m:apply>
		  <m:power/>
		  <m:ci>a</m:ci>
		  <m:cn>2</m:cn>
		</m:apply>
		<m:apply>
		  <m:power/>
		  <m:ci>b</m:ci>
		  <m:cn>2</m:cn>
		</m:apply>
	      </m:apply>
	      <m:apply>
		<m:power/>
		<m:ci>c</m:ci>
		<m:cn>2</m:cn>
	      </m:apply>
	    </m:apply>
	  </m:math></equation><equation id="element-547"><name>Example 2:</name>
	<m:math>
	  <m:apply>
	    <m:eq/>
	    <m:apply>
	      <m:ci type="fn">P</m:ci>
	      <m:ci>f</m:ci>
	    </m:apply>

	    <m:apply>
	      <m:int/>
	      <m:bvar>
		<m:ci>t</m:ci>
	      </m:bvar>
	      <m:lowlimit>
		<m:apply>
		  <m:minus/>
		  <m:infinity/>
		</m:apply>
	      </m:lowlimit>
	      <m:uplimit>
		<m:infinity/>
	      </m:uplimit>
	      <m:apply>
		<m:times/>
		<m:apply>
		  <m:ci type="fn">p</m:ci>
		  <m:ci>t</m:ci>
		</m:apply>
		<m:apply>
		  <m:exp/>
		  <m:apply>
		    <m:minus/>
		    <m:apply>
		      <m:times/>
		      <m:imaginaryi/>
		      <m:cn>2</m:cn>
		      <m:pi/>
		      <m:ci>f</m:ci>
		      <m:ci>t</m:ci>
		    </m:apply>
		  </m:apply>
		</m:apply>
	      </m:apply>
	    </m:apply>

	    <m:apply>
	      <m:int/>
	      <m:bvar>
		<m:ci>t</m:ci>
	      </m:bvar>
	      <m:lowlimit>
		<m:cn>0</m:cn>
	      </m:lowlimit>
	      <m:uplimit>
		<m:ci>Δ</m:ci>
	      </m:uplimit>
	      <m:apply>
		<m:exp/>
		<m:apply>
		  <m:minus/>
		  <m:apply>
		    <m:times/>
		    <m:imaginaryi/>
		    <m:cn>2</m:cn>
		    <m:pi/>
		    <m:ci>f</m:ci>
		    <m:ci>t</m:ci>
		  </m:apply>
		</m:apply>
	      </m:apply>
	    </m:apply>

	    <m:apply>
	      <m:times/>
	      <m:apply>
		<m:divide/>
		<m:cn>1</m:cn>
		<m:apply>
		  <m:minus/>
		  <m:apply>
		    <m:times/>
		    <m:imaginaryi/>
		    <m:cn>2</m:cn>
		    <m:pi/>
		    <m:ci>f</m:ci>
		  </m:apply>
		</m:apply>
	      </m:apply>

	      <m:apply>
		<m:minus/>
		<m:apply>
		  <m:exp/>
		  <m:apply>
		    <m:minus/> 
		    <m:apply>
		      <m:times/>
		      <m:imaginaryi/>
		      <m:cn>2</m:cn>
		      <m:pi/>
		      <m:ci>f</m:ci>
		      <m:ci>Δ</m:ci>
		    </m:apply>
		  </m:apply>
		</m:apply>
		<m:cn>1</m:cn>
	      </m:apply>
	    </m:apply>

	  </m:apply>
	</m:math>
      </equation><equation id="element-287"><name>Example 3: </name>
<m:math>
          <m:apply>
	    <m:diff/>
	    <m:bvar>
	      <m:ci>x</m:ci>
	    </m:bvar>
	    <m:apply>
	      <m:ci type="fn">f</m:ci>
	      <m:ci>x</m:ci>
	    </m:apply>
	  </m:apply>
	</m:math></equation><equation id="element-321"><name>Example 4: </name>
<m:math>
          <m:apply>
            <m:diff/>
	    <m:bvar>
	      <m:ci>x</m:ci>
	      <m:degree><m:cn>2</m:cn></m:degree>
	    </m:bvar>
	    <m:apply><m:ci type="fn">f</m:ci>
	      <m:ci>x</m:ci>
	    </m:apply>
	  </m:apply>
	</m:math></equation><equation id="element-525"><name>Example 5:</name> 
<m:math display="block">
    <m:mstyle displaystyle="true">
        <m:mrow>
        <m:msup> 
        <m:mrow>
        <m:mo> ( </m:mo>       
	  <m:munderover>
            <m:mo>∑</m:mo>
            <m:mrow>
            <m:mi> k </m:mi>
            <m:mo> = </m:mo>
            <m:mn> 1</m:mn>
            </m:mrow>
            <m:mn>n</m:mn>
        </m:munderover>
        <m:msub> 
        <m:mi> a </m:mi> 
        <m:mi> k </m:mi> 
        </m:msub>
        <m:msub> 
        <m:mi> b </m:mi> 
        <m:mi> k </m:mi> 
        </m:msub>
        <m:mo> ) </m:mo>       
        </m:mrow>
        <m:mn> 2 </m:mn> 
        </m:msup>

        <m:mo> ≤ </m:mo>   
    
        <m:mrow>
        <m:mo> ( </m:mo>       
	  <m:munderover>
            <m:mo>∑</m:mo>
            <m:mrow>
            <m:mi> k </m:mi>
            <m:mo> = </m:mo>
            <m:mn> 1</m:mn>
            </m:mrow>
            <m:mn>n</m:mn>
        </m:munderover>
        <m:msup>
        <m:mrow>
        <m:msub> 
        <m:mi> a </m:mi>
        <m:mi> k </m:mi>
        </m:msub>
        </m:mrow>
        <m:mn> 2 </m:mn>
        </m:msup>
        <m:mo> ) </m:mo>       
        </m:mrow>

        <m:mrow>
        <m:mo> ( </m:mo>       
	  <m:munderover>
          <m:mo>∑</m:mo>
            <m:mrow>
            <m:mi> k </m:mi>
            <m:mo> = </m:mo>
            <m:mn> 1</m:mn>
            </m:mrow>
          <m:mn>n</m:mn>
        </m:munderover>
        <m:msup>
        <m:mrow>
        <m:msub> 
        <m:mi> b </m:mi>
        <m:mi> k </m:mi>
        </m:msub>
        </m:mrow>
        <m:mn> 2 </m:mn>
        </m:msup>
        <m:mo> ) </m:mo> 
        </m:mrow>
      </m:mrow>
   </m:mstyle>
</m:math> 
</equation><equation id="element-868"><name>Example 6:</name>  
<m:math>
         <m:mi> x </m:mi>
         <m:mo> = </m:mo>

              <m:mrow> 
         <m:mo> [ </m:mo>
         <m:mn> 32000 </m:mn> 
         <m:mo> ( </m:mo> 
         <m:mn> 1 </m:mn> 
         <m:mo> - </m:mo>
           <m:mfrac linethickness="2"> 
            <m:mn> 5 </m:mn> 
            <m:mn> 100 </m:mn> 
           </m:mfrac>
         <m:mo> ) </m:mo> 
         <m:mo> ( </m:mo> 
   <m:mn> 1 </m:mn> 
         <m:mo> + </m:mo>
           <m:mfrac linethickness="2"> 
            <m:mn> 10 </m:mn> 
            <m:mn> 100 </m:mn> 
           </m:mfrac>
         <m:mo> ) </m:mo> 
         <m:mo> ( </m:mo> 
   <m:mn> 1 </m:mn> 
         <m:mo> + </m:mo>
           <m:mfrac linethickness="2"> 
              <m:mrow> 
              <m:mfrac> 
              <m:mn> 25 </m:mn>
              <m:mn> 2 </m:mn>
              </m:mfrac> 
              </m:mrow> 
            <m:mn> 100 </m:mn> 
           </m:mfrac>
         <m:mo> ) </m:mo> 
         <m:mo> ] </m:mo> 
              </m:mrow> 
   </m:math>
</equation><equation id="element-700"><name>Example 7: </name>
<m:math>
          <m:matrix>
	    <m:matrixrow>
	      <m:ci>a</m:ci>
	      <m:ci>b</m:ci>
	      <m:ci>c</m:ci>
	    </m:matrixrow>
	    <m:matrixrow>
	      <m:ci>d</m:ci>
	      <m:ci>e</m:ci>
	      <m:ci>f</m:ci>
	    </m:matrixrow>
	    <m:matrixrow>
	      <m:ci>g</m:ci>
	      <m:ci>h</m:ci>
	      <m:ci>j</m:ci>
	    </m:matrixrow>
	  </m:matrix>
	</m:math></equation><para id="delete_me">
       <!-- Insert module text here -->
    </para>   
  </content>
  
</document>
