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1、7.4.2三重积分的计算II.利用柱面坐标和球面坐标计算三重积分TripleIntegralsinCylindricalandSphericalCoordinates柱面坐标CylindricalCoordinates柱面坐标＝极坐标＋竖坐标柱面坐标规定：柱面坐标的三组坐标面常数圆柱面：常数柱面坐标因此得名常数半平面常数平面with(plots):x_axis:=plot3d([u,0,0],u=0..2,v=0..0.01,thickness=2):y_axis:=plot3d([0,u,0],u=0..2,v=0..0.01,thickness=2):z
2、_axis:=plot3d([0,0,u],u=0..11,v=0..0.01,thickness=2):forifrom1to40dopingmian[i]:=plot3d([t,s,i/4],t=0..2,s=0..2,color=blue,style=patchnogrid):od:pingmian:=display(seq(pingmian[i],i=1..40),insequence=true):display(pingmian,x_axis,y_axis,z_axis,orientation=[24,67]);柱面坐标的坐标面柱面坐标的坐标面动画
3、runinMaplewith(plots):x_axis:=plot3d([u,0,0],u=0..2,v=0..0.01,thickness=2):y_axis:=plot3d([0,u,0],u=0..2,v=0..0.01,thickness=2):z_axis:=plot3d([0,0,u],u=0..2.3,v=0..0.01,thickness=2):forifrom1to40dozhumian[i]:=plot3d([2*i/40,theta,z],theta=0..2*Pi,z=0..2,color=green,style=patch,coo
4、rds=cylindrical):pingmian[i]:=plot3d([x,y,2*i/40],x=-2..2,y=-2..2,color=blue,style=patchnogrid):banpingmian[i]:=plot3d([r,2*Pi*i/40,z],r=0..3,z=0..2,color=brown,style=patchnogrid,coords=cylindrical):od:banpingmian:=display(seq(banpingmian[i],i=1..40),insequence=true):pingmian:=disp
5、lay(seq(pingmian[i],i=1..40),insequence=true):zhumian:=display(seq(zhumian[i],i=1..40),insequence=true):display(pingmian,banpingmian,zhumian,x_axis,y_axis,z_axis,orientation=[24,67]);用以上三组坐标面划分区域两张相邻的水平面两个相邻的圆柱面两张相邻的半平面with(plots):x_axis:=plot3d([u,0,0],u=0..3,v=0..0.01,thickness=2
6、):y_axis:=plot3d([0,u,0],u=0..3,v=0..0.01,thickness=2):z_axis:=plot3d([0,0,u],u=0..3.3,v=0..0.01,thickness=2):banpingmian1:=plot3d([r,Pi/6,z],r=0..3,z=0..2,coords=cylindrical,style=patch,color=green):banpingmian2:=plot3d([r,Pi/3,z],r=0..3,z=0..2,coords=cylindrical,style=patch,color
7、=green):zhumian1:=plot3d([1,theta,z],theta=0..2*Pi,z=0..2,coords=cylindrical,style=patch,color=red):zhumian2:=plot3d([2,theta,z],theta=0..2*Pi,z=0..2,coords=cylindrical,style=patch,color=red):pingmian1:=plot3d([r,theta,1],r=0..3,theta=0..2*Pi,coords=cylindrical,style=patch,color=bl
8、ue):pingmian2:=plot3d([r,t
