工程电磁场-矢量分析.ppt
,1,工程电磁场,2,3,4,标量:,矢量:,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,根据矢量线的定义,在矢量线上任一点的切向矢量元dl与矢量场平行,即:,在直角坐标系中有,26,27,28,29,30,31,几个重要物理量及公式,32,方向导数 梯度 通量密度 散度 环量密度 旋度,矢量场,标量场,黄色:标量 红色:矢量,场是否有源,场是否有旋,场的边界,两个重要公式,2023/9/9,33,2023/9/9,34,在高等数学中 什么是导数?导数定义在哪个方向?,方向导数的通俗解释是:我们不仅要知道函数在坐标轴方向上的变化率(即偏导数),而且还要设法求得函数在其他特定方向上的变化率(即方向导数)。方向导数就是函数在其他特定方向上的变化率。,当自变量的增量趋于零时,因变量的增量与自变量的增量之商的极限。,2023/9/9,35,思考:对M0,M点有何要求?,2023/9/9,36,2023/9/9,37,2023/9/9,38,2023/9/9,39,2023/9/9,40,定义与计算方法的差别,思考:为何要求可微?,2023/9/9,41,2023/9/9,42,2023/9/9,43,2023/9/9,44,梯度:回答这两个问题,2023/9/9,45,2023/9/9,46,2023/9/9,47,标量,2023/9/9,48,2023/9/9,49,2023/9/9,50,2023/9/9,51,2023/9/9,52,矢量,2023/9/9,53,2023/9/9,54,2023/9/9,55,2023/9/9,56,2023/9/9,57,2023/9/9,58,2023/9/9,59,若 S 为闭合曲面 根据通量的大小判断闭合面中源的性质:,2023/9/9,60,2023/9/9,61,2023/9/9,62,2023/9/9,63,散度:单位体积的通量,2023/9/9,64,2023/9/9,65,2023/9/9,66,2023/9/9,67,2023/9/9,68,2023/9/9,69,2023/9/9,70,2023/9/9,71,2023/9/9,72,2023/9/9,73,2023/9/9,74,2023/9/9,75,2023/9/9,76,2023/9/9,77,2023/9/9,78,2023/9/9,79,2023/9/9,80,2023/9/9,81,2023/9/9,82,2023/9/9,83,2023/9/9,84,2023/9/9,85,梯度在某个方向上的投影,就是在这个方向上的方向导数。,2023/9/9,86,分别计算三个方向上的旋度,2023/9/9,87,2023/9/9,88,2023/9/9,89,2023/9/9,90,2023/9/9,91,2023/9/9,92,2023/9/9,93,2023/9/9,94,2023/9/9,95,2023/9/9,96,2023/9/9,97,2023/9/9,98,2023/9/9,99,2023/9/9,100,2023/9/9,101,2023/9/9,102,2023/9/9,103,2023/9/9,104,2023/9/9,105,2023/9/9,106,2023/9/9,107,2023/9/9,108,2023/9/9,109,2023/9/9,110,2023/9/9,111,2023/9/9,112,2023/9/9,113,2023/9/9,114,2023/9/9,115,2023/9/9,116,2023/9/9,117,2023/9/9,118,2023/9/9,119,2023/9/9,120,2023/9/9,121,7.亥姆霍兹定理 在空间有限区域V内的某一矢量场F,由它的散度、旋度和边界条件唯一地确定。,2023/9/9,122,2023/9/9,123,2023/9/9,124,2023/9/9,125,2023/9/9,126,2023/9/9,127,2023/9/9,128,2023/9/9,129,2023/9/9,130,2023/9/9,131,2023/9/9,132,2023/9/9,133,2023/9/9,134,2023/9/9,135,2023/9/9,136,2023/9/9,137,2023/9/9,138,2023/9/9,139,2023/9/9,140,2023/9/9,141,2023/9/9,142,2023/9/9,143,2023/9/9,144,2,2,2,2,2023/9/9,145,2023/9/9,146,2023/9/9,147,本章结束,