ppt课件(6-9,16章).zip
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ppt课件(6-9,16章).zip <link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/base.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/css/fancy.min.css" rel="stylesheet"/><link href="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89493304/raw.css" rel="stylesheet"/><div id="sidebar" style="display: none"><div id="outline"></div></div><div class="pf w0 h0" data-page-no="1" id="pf1"><div class="pc pc1 w0 h0"><img alt="" class="bi x0 y0 w1 h1" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89493304/bg1.jpg"/><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">数学分析（<span class="ff2">2</span>）</div><div class="t m0 x2 h3 y2 ff3 fs1 fc1 sc0 ls0 ws0">1</div><div class="t m0 x3 h4 y3 ff1 fs1 fc1 sc0 ls0 ws0">华北科技学院理学院</div><div class="t m0 x4 h3 y4 ff3 fs1 fc1 sc0 ls0 ws0">6/28/2024</div><div class="t m0 x5 h5 y5 ff1 fs2 fc1 sc0 ls0 ws0">四、小结</div><div class="t m0 x6 h6 y6 ff4 fs2 fc1 sc0 ls0 ws0">一、定积分的微元法</div><div class="t m0 x6 h6 y7 ff4 fs2 fc1 sc0 ls0 ws0">二、定积分在物理上的应用</div><div class="t m0 x6 h6 y8 ff4 fs2 fc1 sc0 ls0 ws0">三、简单数学模型和求解</div><a class="l"><div class="d m1"></div></a><a class="l"><div class="d m1"></div></a><a class="l"><div class="d m1"></div></a><a class="l"><div class="d m1"></div></a></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div><div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89493304/bg2.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">数学分析（<span class="ff2">2</span>）</div><div class="t m0 x7 h3 y9 ff3 fs1 fc1 sc0 ls0 ws0">2</div><div class="t m0 x8 h4 ya ff1 fs1 fc1 sc0 ls0 ws0">华北科技学院理学院</div><div class="t m0 x9 h3 y9 ff3 fs1 fc1 sc0 ls0 ws0">6/28/2024</div><div class="t m0 xa h7 yb ff5 fs1 fc1 sc0 ls0 ws0">5-1-2</div><div class="t m0 xb h6 yc ff4 fs2 fc2 sc0 ls0 ws0">一、定积分的微元法</div><div class="t m0 xc h8 yd ff1 fs3 fc1 sc0 ls0 ws0">用定积分计算的量应具有如下</div><div class="t m0 xd h8 ye ff1 fs3 fc1 sc0 ls0 ws0">许多部分区间<span class="ff3">,</span></div><div class="t m0 xe h8 yf ff3 fs3 fc1 sc0 ls0 ws0">(<span class="ff1">即把</span>[<span class="ff6">a<span class="_ _0"></span><span class="ff3">, <span class="ff6">b</span>]<span class="ff1">分成</span></span></span></div><div class="t m2 xf h9 y10 ff7 fs4 fc3 sc0 ls0 ws0">两个特点</div><div class="t m0 x10 ha y10 ff6 fs3 fc3 sc0 ls0 ws0">:</div><div class="t m0 x11 h8 y11 ff3 fs3 fc1 sc0 ls0 ws0">(1) <span class="ff1">所求量<span class="ff6">I </span>即与</span>[<span class="ff6">a<span class="_ _0"></span><span class="ff3">, <span class="ff6">b</span>]<span class="ff1">有关</span>;</span></span></div><div class="t m0 x12 h8 y12 ff3 fs3 fc1 sc0 ls0 ws0">(2) <span class="ff6">I <span class="ff1">在</span></span>[<span class="ff6">a<span class="_ _0"></span><span class="ff3">, <span class="ff6">b</span>]<span class="ff1">上具有可加性</span>.</span></span></div><div class="t m0 x13 h8 y13 ff1 fs3 fc1 sc0 ls0 ws0">则<span class="ff6">I </span>相应地分成许多部分量<span class="ff3">,</span></div><div class="t m0 xd h8 y14 ff1 fs3 fc1 sc0 ls0 ws0">而<span class="ff6">I </span>等于所有部分量之和<span class="ff3">)</span></div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div><div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89493304/bg3.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">数学分析（<span class="ff2">2</span>）</div><div class="t m0 x7 h3 y9 ff3 fs1 fc1 sc0 ls0 ws0">3</div><div class="t m0 x8 h4 ya ff1 fs1 fc1 sc0 ls0 ws0">华北科技学院理学院</div><div class="t m0 x9 h3 y9 ff3 fs1 fc1 sc0 ls0 ws0">6/28/2024</div><div class="t m0 x14 h8 y15 ff3 fs3 fc1 sc0 ls0 ws0">(1) <span class="ff1">求微元</span> <span class="ff1">局部近似得</span> <span class="fc0">d<span class="ff6">U</span> = <span class="ff6">f <span class="_ _1"></span></span>(<span class="ff6">x<span class="_ _1"></span></span>)d<span class="ff6">x</span></span></div><div class="t m0 x15 h8 y16 ff3 fs3 fc1 sc0 ls0 ws0">(2) <span class="ff1">求全量</span> <span class="ff1">微元积分得</span></div><div class="t m0 x16 hb y17 ff4 fs3 fc4 sc0 ls0 ws0">应用方向：</div><div class="t m0 x15 h8 y18 ff1 fs3 fc1 sc0 ls0 ws0">　　平面图形的面积；体积；平面曲线的弧长；物理中的</div><div class="t m0 x15 h8 y19 ff1 fs3 fc1 sc0 ls0 ws0">应用等．</div><div class="t m0 x17 h6 y1a ff4 fs2 fc2 sc0 ls0 ws0">微元法过程：</div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div><div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89493304/bg4.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">数学分析（<span class="ff2">2</span>）</div><div class="t m0 x18 h3 y9 ff3 fs1 fc1 sc0 ls0 ws0">4</div><div class="t m0 x8 h4 ya ff1 fs1 fc1 sc0 ls0 ws0">华北科技学院理学院</div><div class="t m0 x7 h3 y9 ff3 fs1 fc1 sc0 ls0 ws0">6/28/2024</div><div class="t m0 x19 ha y1b ff3 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">1</span></div><div class="t m0 x1a ha y1c ff3 fs3 fc1 sc0 ls0 ws0">1</div><div class="t m0 x1b hb y1d ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">）</span></div><div class="t m0 x1c hb y1c ff4 fs3 fc1 sc0 ls0 ws0">）</div><div class="t m0 x1d ha y1e ff3 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">2</span></div><div class="t m0 x17 ha y1f ff3 fs3 fc1 sc0 ls0 ws0">2</div><div class="t m0 x1e hb y20 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">）</span></div><div class="t m0 x1f hb y1f ff4 fs3 fc1 sc0 ls0 ws0">）</div><div class="t m0 x20 hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">在</span></div><div class="t m0 x21 hb y22 ff4 fs3 fc1 sc0 ls0 ws0">在</div><div class="t m0 x22 hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">区</span></div><div class="t m0 x23 hb y22 ff4 fs3 fc1 sc0 ls0 ws0">区</div><div class="t m0 x24 hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">间</span></div><div class="t m0 x25 hb y22 ff4 fs3 fc1 sc0 ls0 ws0">间</div><div class="t m0 x26 hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">内</span></div><div class="t m0 x13 hb y22 ff4 fs3 fc1 sc0 ls0 ws0">内</div><div class="t m0 x27 hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">，</span></div><div class="t m0 x28 hb y22 ff4 fs3 fc1 sc0 ls0 ws0">，</div><div class="t m0 x29 hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">任</span></div><div class="t m0 x2a hb y22 ff4 fs3 fc6 sc0 ls0 ws0">任</div><div class="t m0 x2b hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">取</span></div><div class="t m0 x2c hb y22 ff4 fs3 fc6 sc0 ls0 ws0">取</div><div class="t m0 x2d hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">一</span></div><div class="t m0 x2e hb y22 ff4 fs3 fc6 sc0 ls0 ws0">一</div><div class="t m0 xe hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">小</span></div><div class="t m0 x2f hb y22 ff4 fs3 fc6 sc0 ls0 ws0">小</div><div class="t m0 xf hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">区</span></div><div class="t m0 x30 hb y22 ff4 fs3 fc6 sc0 ls0 ws0">区</div><div class="t m0 x31 hb y21 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">间</span></div><div class="t m0 x32 hb y22 ff4 fs3 fc6 sc0 ls0 ws0">间</div><div class="t m0 x33 hb y23 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">求</span></div><div class="t m0 x34 hb y24 ff4 fs3 fc1 sc0 ls0 ws0">求</div><div class="t m0 x35 hb y23 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">出</span></div><div class="t m0 x36 hb y24 ff4 fs3 fc1 sc0 ls0 ws0">出</div><div class="t m0 x37 hb y25 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">相</span></div><div class="t m0 x38 hb y26 ff4 fs3 fc1 sc0 ls0 ws0">相</div><div class="t m0 x39 hb y25 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">应</span></div><div class="t m0 x3a hb y26 ff4 fs3 fc1 sc0 ls0 ws0">应</div><div class="t m0 x3b hb y25 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">于</span></div><div class="t m0 x3c hb y26 ff4 fs3 fc1 sc0 ls0 ws0">于</div><div class="t m0 x3d hb y25 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">该</span></div><div class="t m0 x3e hb y26 ff4 fs3 fc1 sc0 ls0 ws0">该</div><div class="t m0 x3f hb y25 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">区</span></div><div class="t m0 x40 hb y26 ff4 fs3 fc1 sc0 ls0 ws0">区</div><div class="t m0 x41 hb y25 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">间</span></div><div class="t m0 x42 hb y26 ff4 fs3 fc1 sc0 ls0 ws0">间</div><div class="t m0 x43 hb y25 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">上</span></div><div class="t m0 x44 hb y26 ff4 fs3 fc1 sc0 ls0 ws0">上</div><div class="t m0 x45 hb y25 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">的</span></div><div class="t m0 x46 hb y26 ff4 fs3 fc1 sc0 ls0 ws0">的</div><div class="t m0 x47 hb y25 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">微</span></div><div class="t m0 x48 hb y26 ff4 fs3 fc6 sc0 ls0 ws0">微</div><div class="t m0 x49 hb y25 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">元</span></div><div class="t m0 x4a hb y26 ff4 fs3 fc6 sc0 ls0 ws0">元</div><div class="t m0 x1d ha y27 ff3 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">3</span></div><div class="t m0 x17 ha y28 ff3 fs3 fc1 sc0 ls0 ws0">3</div><div class="t m0 x1e hb y29 ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">）</span></div><div class="t m0 x1f hb y28 ff4 fs3 fc1 sc0 ls0 ws0">）</div><div class="t m0 x37 hb y2a ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">写</span></div><div class="t m0 x38 hb y2b ff4 fs3 fc6 sc0 ls0 ws0">写</div><div class="t m0 x39 hb y2a ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">出</span></div><div class="t m0 x3a hb y2b ff4 fs3 fc6 sc0 ls0 ws0">出</div><div class="t m0 x3b hb y2a ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">定</span></div><div class="t m0 x3c hb y2b ff4 fs3 fc6 sc0 ls0 ws0">定</div><div class="t m0 x3d hb y2a ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">积</span></div><div class="t m0 x3e hb y2b ff4 fs3 fc6 sc0 ls0 ws0">积</div><div class="t m0 x3f hb y2a ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">分</span></div><div class="t m0 x40 hb y2b ff4 fs3 fc6 sc0 ls0 ws0">分</div><div class="t m0 x41 hb y2a ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">的</span></div><div class="t m0 x42 hb y2b ff4 fs3 fc6 sc0 ls0 ws0">的</div><div class="t m0 x43 hb y2a ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">表</span></div><div class="t m0 x44 hb y2b ff4 fs3 fc6 sc0 ls0 ws0">表</div><div class="t m0 x45 hb y2a ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">达</span></div><div class="t m0 x46 hb y2b ff4 fs3 fc6 sc0 ls0 ws0">达</div><div class="t m0 x47 hb y2a ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">式</span></div><div class="t m0 x48 hb y2b ff4 fs3 fc6 sc0 ls0 ws0">式</div><div class="t m0 x49 hb y2a ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">：</span></div><div class="t m0 x4a hb y2b ff4 fs3 fc6 sc0 ls0 ws0">：</div><div class="t m0 x4b hb y2c ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">定</span></div><div class="t m0 x4c hb y2d ff4 fs3 fc3 sc0 ls0 ws0">定</div><div class="t m0 x4d hb y2c ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">积</span></div><div class="t m0 x4e hb y2d ff4 fs3 fc6 sc0 ls0 ws0">积</div><div class="t m0 x4f hb y2c ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">分</span></div><div class="t m0 x50 hb y2d ff4 fs3 fc6 sc0 ls0 ws0">分</div><div class="t m0 x51 hb y2c ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">区</span></div><div class="t m0 x52 hb y2d ff4 fs3 fc6 sc0 ls0 ws0">区</div><div class="t m0 x53 hb y2c ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">间</span></div><div class="t m0 x54 hb y2d ff4 fs3 fc6 sc0 ls0 ws0">间</div><div class="t m0 x55 hb y2e ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">选</span></div><div class="t m0 x56 hb y2f ff4 fs3 fc1 sc0 ls0 ws0">选</div><div class="t m0 x6 hb y2e ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">积</span></div><div class="t m0 x57 hb y2f ff4 fs3 fc6 sc0 ls0 ws0">积</div><div class="t m0 x58 hb y2e ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">分</span></div><div class="t m0 x59 hb y2f ff4 fs3 fc6 sc0 ls0 ws0">分</div><div class="t m0 x5a hb y2e ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">变</span></div><div class="t m0 x5b hb y2f ff4 fs3 fc6 sc0 ls0 ws0">变</div><div class="t m0 x5c hb y2e ff4 fs3 fc5 sc0 ls0 ws0"><span class="fc7 sc0">量</span></div><div class="t m0 x5d hb y2f ff4 fs3 fc6 sc0 ls0 ws0">量</div><div class="t m0 x5e hb y30 ff4 fs3 fc3 sc0 ls0 ws0">应用定积分的微元法解决问题的具体步骤是：</div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div><div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="/image.php?url=https://csdnimg.cn/release/download_crawler_static/89493304/bg5.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">数学分析（<span class="ff2">2</span>）</div><div class="t m0 x5f h5 y31 ff1 fs2 fc1 sc0 ls0 ws0">二、定积分<span class="ff2"> </span>在物理上的应用</div><div class="t m0 x60 h8 y32 ff1 fs3 fc1 sc0 ls0 ws0">例<span class="ff3">1. </span><span class="fc3">（不均匀金属棒的质量问题）</span></div><div class="t m0 x60 h8 y33 ff1 fs3 fc1 sc0 ls0 ws0">如图一根金属棒，其密度分布为</div><div class="t m0 x60 h8 y34 ff1 fs3 fc1 sc0 ls0 ws0">求这根金属棒的质量<span class="ff3">M.</span></div><div class="t m0 x61 hb y35 ff4 fs3 fc8 sc0 ls0 ws0">解：取<span class="ff2"> </span>为积分变量，<span class="ff2"><span class="fc7 sc0"> </span></span></div><div class="t m0 x62 hb y36 ff4 fs3 fc1 sc0 ls0 ws0">在<span class="ff2">[0,6]</span>上，任取一个小区间<span class="ff2"><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span><span class="fc7 sc0"> </span></span>得质量元素</div><div class="t m0 x63 hc y37 ff8 fs3 fc0 sc0 ls0 ws0">x<span class="_ _2"> </span>x+dx</div><div class="t m0 x64 hc y38 ff8 fs3 fc0 sc0 ls0 ws0">x</div><div class="t m0 x61 hd y39 ff2 fs3 fc8 sc0 ls0 ws0"> </div><div class="t m0 x62 hb y3a ff4 fs3 fc1 sc0 ls0 ws0">从而，得质量</div><div class="t m0 x34 h8 y3b ff1 fs3 fc1 sc0 ls0 ws0">线密度</div></div><div class="pi" data-data='{"ctm":[1.333333,0.000000,0.000000,1.333333,0.000000,0.000000]}'></div></div>