吉林建筑工程学院学报
吉林建築工程學院學報
길림건축공정학원학보
JOURNAL OF JILIN ARCHITECTURAL AND CIVIL ENGINEERING INSTITUTE
2012年
6期
74-76
,共3页
微元法%球面坐标%柱面坐标%对面积的曲面积分
微元法%毬麵坐標%柱麵坐標%對麵積的麯麵積分
미원법%구면좌표%주면좌표%대면적적곡면적분
infinitesimal method%spherical coordinates%cylindrical coordinates%curved surface integral to area
对面积的曲面积分∫∫∑f（x,y,z）ds计算一般方法是按曲面所给方程情况的不同，来决定积分曲面向哪个坐标面投影并根据投影后的平面区域情况转化为二重积分．如果曲面方程是以球面或柱面形式给出，设法转化为二重积分，这种直接计算方法有时比较麻烦．本文利用微元法把曲面微元转化成两个变量微分之积，利用球面、柱面坐标与直角坐标之间的关系，对面积的曲面积分∫∫∑f（x,y,z）ds计算方便快捷，效果较好，值得在教学中推广．
對麵積的麯麵積分∫∫∑f（x,y,z）ds計算一般方法是按麯麵所給方程情況的不同，來決定積分麯麵嚮哪箇坐標麵投影併根據投影後的平麵區域情況轉化為二重積分．如果麯麵方程是以毬麵或柱麵形式給齣，設法轉化為二重積分，這種直接計算方法有時比較痳煩．本文利用微元法把麯麵微元轉化成兩箇變量微分之積，利用毬麵、柱麵坐標與直角坐標之間的關繫，對麵積的麯麵積分∫∫∑f（x,y,z）ds計算方便快捷，效果較好，值得在教學中推廣．
대면적적곡면적분∫∫∑f（x,y,z）ds계산일반방법시안곡면소급방정정황적불동，래결정적분곡면향나개좌표면투영병근거투영후적평면구역정황전화위이중적분．여과곡면방정시이구면혹주면형식급출，설법전화위이중적분，저충직접계산방법유시비교마번．본문이용미원법파곡면미원전화성량개변량미분지적，이용구면、주면좌표여직각좌표지간적관계，대면적적곡면적분∫∫∑f（x,y,z）ds계산방편쾌첩，효과교호，치득재교학중추엄．
Curved surface integral with respect to area calculation method is given according to the curved surface e-quation is different, to determine the integral curved surface which coordinate plane projection according to the pro-jection region into the double integral. To if the surface is spherical or cylindrical part, manage to convert multiple integral. The direct calculation method is sometimes more trouble; the infinitesimal method the surface element into two variable differential products, the use the relationship of spherical, cylindrical coordinates and rectangular coor-dinates, on the surface integral calculation is simplified, good effect, is worth in the teaching.
