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<title> 二次函数法 </title>
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<font COLOR="#0000FF">
<h1>9.1.2 二次函数法</h1>
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<p><font FACE="Times New Roman">MATLAB </font>另外提供二种积分函数，它们分别是辛普森法
<font COLOR="#FF0000" FACE="Times New Roman">quad</font><font FACE="Times New Roman"> </font>和牛顿<font FACE="Times New Roman">-</font>康兹法 <font COLOR="#FF0000" FACE="Times New Roman">quad8</font>。三种方法的精确度由低
而高，分别为 <font COLOR="#FF0000" FACE="Times New Roman">trapz</font><font FACE="Times New Roman">,</font><font COLOR="#FF0000" FACE="Times New Roman"> quad</font><font FACE="Times New Roman">,</font><font COLOR="#FF0000" FACE="Times New Roman"> quad8</font>。<br>
</p>
<p>由于这二种方法依据的积分法不同于梯形法，因此它们的语法就和
<font COLOR="#FF0000" FACE="Times New Roman">trapz</font><font FACE="Times New Roman"> </font>不同；其语法为
<font COLOR="#FF0000" FACE="Times New Roman">quad('function',a,b)</font> （<font COLOR="#FF0000" FACE="Times New Roman">quad8</font>语法相同），其中<font COLOR="#FF0000" FACE="Times New Roman">function</font>是一已定义函数的名称（如<font COLOR="#FF0000" FACE="Times New Roman">sin</font><font FACE="Times New Roman">, </font><font COLOR="#FF0000" FACE="Times New Roman">cos</font><font FACE="Times New Roman">, </font><font COLOR="#FF0000" FACE="Times New Roman">sqrt</font><font FACE="Times New Roman">, </font><font COLOR="#FF0000" FACE="Times New Roman">log</font><font FACE="Times New Roman"> </font>等），而
<font COLOR="#FF0000" FACE="Times New Roman">a</font><font FACE="Times New Roman">, </font><font COLOR="#FF0000" FACE="Times New Roman">b</font>是积分的下限和 上限。和 <font COLOR="#FF0000" FACE="Times New Roman">trapz</font>比较，<font COLOR="#FF0000" FACE="Times New Roman">quad</font><font FACE="Times New Roman">, </font><font COLOR="#FF0000" FACE="Times New Roman">quad8</font>不同之处在于这二者类似解析式的积分式，只须设定上下限及定义要积分
的函数；而 <font COLOR="#FF0000" FACE="Times New Roman">trapz</font>则是针对离散点型态的数据做积分。
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<p>我们看一简单积分式 </p>
<p><img SRC="../img9/img00003.gif" tppabs="http://webclass.ncu.edu.tw/~junwu/img9/img00003.gif" WIDTH="194" HEIGHT="44"> </p>
<p>以下为 <font FACE="Times New Roman">MATLAB </font>的程式 </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> a=0; b=0.5;</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> kq=quad('sqrt',a,b)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">kq =</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">0.2357</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> kq8=quad8('sqrt',a,b)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">kq8 =</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">0.2357<br>
</font></p>
<p>再来看一个较复杂的积分式 </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> x=-1:0.17:2;</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> y=humps(x);</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> area=trapz(x,y)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">area =</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">25.9174</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> x=-1:0.07:2;</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> y=humps(x);</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> area=trapz(x,y)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">area =</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">26.6243</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> area=quad('hump',-1,2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">area =</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">26.3450</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">>> area=quad8('hump',-1,2)</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">area =</font> </p>
<p><font COLOR="#FF0000" FACE="Times New Roman">26.3450<br>
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