曲線積分與曲面積分習(xí)題課課件

1、第十章 曲線積分與曲面積分 一、主要內(nèi)容二、典型例題安徽財(cái)經(jīng)大學(xué) Anhui University of Finance& Economics（一）曲線積分與曲面積分（二）各種積分之間的聯(lián)系（三）場(chǎng)論初步 一、主要內(nèi)容曲線積分曲面積分對(duì)面積的曲面積分對(duì)坐標(biāo)的曲面積分對(duì)弧長(zhǎng)的曲線積分對(duì)坐標(biāo)的曲線積分定義計(jì)算定義計(jì)算聯(lián)系聯(lián)系（一）曲線積分與曲面積分一、主要內(nèi)容 曲 線 積 分對(duì)弧長(zhǎng)的曲線積分對(duì)坐標(biāo)的曲線積分定義聯(lián)系計(jì)算三代一定二代一定 (與方向有關(guān))一、主要內(nèi)容與路徑無(wú)關(guān)的四個(gè)等價(jià)命題條件等價(jià)命題一、主要內(nèi)容 曲 面 積 分對(duì)面積的曲面積分對(duì)坐標(biāo)的曲面積分定義聯(lián)系計(jì) 算一代,二換,三投(與側(cè)無(wú)關(guān))

2、一代,二投,三定向 (與側(cè)有關(guān))一、主要內(nèi)容定積分曲線積分重積分曲面積分計(jì)算計(jì)算計(jì)算Green公式Stokes公式Guass公式（二）各種積分之間的聯(lián)系一、主要內(nèi)容積分概念的聯(lián)系定積分二重積分一、主要內(nèi)容曲面積分曲線積分三重積分曲線積分一、主要內(nèi)容計(jì)算上的聯(lián)系一、主要內(nèi)容其中一、主要內(nèi)容理論上的聯(lián)系牛頓-萊布尼茨公式格林公式一、主要內(nèi)容高斯公式斯托克斯公式一、主要內(nèi)容Green公式,Guass公式,Stokes公式之間的關(guān)系或推廣推廣一、主要內(nèi)容梯度通量旋度環(huán)流量散度（三）場(chǎng)論初步一、主要內(nèi)容思路:閉合非閉閉合非閉補(bǔ)充曲線或用公式二、典型例題解二、典型例題解(如下圖)二、典型例題二、典型例題曲

3、面面積的計(jì)算法SDxy二、典型例題曲頂柱體的表面積 如圖曲頂柱體，二、典型例題解由對(duì)稱性二、典型例題二、典型例題例解利用兩類曲面積分之間的關(guān)系二、典型例題二、典型例題向量點(diǎn)積法二、典型例題例解利用向量點(diǎn)積法二、典型例題二、典型例題解(如下圖)二、典型例題二、典型例題二、典型例題測(cè)驗(yàn)題測(cè)驗(yàn)題答案Ioo%n$HmlZiWUxa7J0Bx7RL9x&Ws)XhA$PgQAY1n3y$FW$7Q3o&307HV-uuifFKM-XBnCvnxbMmp6VTjI5*ywNqg)m)L6+41Fxq2bwKwEPI-C)1sV)Gs7u4Rc5cbSNLrF)ibrLNe$zPj#g461*37tgZFN

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