直角坐标坐标面

10.3三重积分

1用动画显示

直角坐标的坐标面第1页/共7页第一页，共8页。10.3三重积分

2直角坐标的坐标面with(plots):K:=40:forifrom0toKdoti:=-2+4*i/K:pingmian1[i]:=plot3d([x,y,ti],x=-2..2,y=-2..2,color=blue):pingmian2[i]:=plot3d([x,ti,z],x=-2..2,z=-2..2,color=yellow):pingmian3[i]:=plot3d([ti,y,z],y=-2..2,z=-2..2,color=green):pingmian[i]:=display({pingmian1[i],pingmian2[i],pingmian3[i]},style=patchnogrid)od:pingmian:=display(seq(pingmian[i],i=0..K),insequence=true):x_axis:=plot3d([u,0,0],u=-2.5..2.5,v=0..0.01):y_axis:=plot3d([0,u,0],u=-2.5..2.5,v=0..0.01):z_axis:=plot3d([0,0,u],u=-2.5..2.5,v=0..0.01):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(pingmian,xyz,orientation=[40,60],lightmodel=light2,tickmarks=[4,4,4],title="XUXZJULY2009");第2页/共7页第二页，共8页。10.3三重积分

3with(plots):K:=40:forifrom0toKdoti:=-Pi+i*2*Pi/K:pingmian1[i]:=plot3d([x,y,sin(ti)],x=-2..2,y=-2..2,color=blue):pingmian2[i]:=plot3d([x,sin(ti+Pi/8),z],x=-2..2,z=-2..2,color=yellow):pingmian3[i]:=plot3d([sin(ti-Pi/6),y,z],y=-2..2,z=-2..2,color=green):pingmian[i]:=display({pingmian1[i],pingmian2[i],pingmian3[i]},style=patchnogrid)od:pingmian:=display(seq(pingmian[i],i=0..K),insequence=true):x_axis:=plot3d([u,0,0],u=-2.5..2.5,v=0..0.01):y_axis:=plot3d([0,u,0],u=-2.5..2.5,v=0..0.01):z_axis:=plot3d([0,0,u],u=-2.5..2.5,v=0..0.01):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(pingmian,xyz,orientation=[40,60],lightmodel=light2,tickmarks=[4,4,4],title="XUXZJULY2009");第3页/共7页第三页，共8页。10.3三重积分

4直角坐标系中的体积元素with(plots):x1:=1:x2:=2:y1:=1:y2:=2:z1:=1:z2:=2:pingmian1:=plot3d([x,y,z1],x=x1..x2,y=y1..y2,color=blue):pingmian12:=plot3d([x,y,z2],x=x1..x2,y=y1..y2,color=blue):pingmian2:=plot3d([x,y1,z],x=x1..x2,z=z1..z2,color=yellow):pingmian22:=plot3d([x,y2,z],x=x1..x2,z=z1..z2,color=yellow):pingmian3:=plot3d([x1,y,z],y=y1..y2,z=z1..z2,color=green):pingmian32:=plot3d([x2,y,z],y=y1..y2,z=z1..z2,color=green):pingmian:=display({pingmian1,pingmian12,pingmian2,pingmian22,pingmian3,pingmian32},style=patchnogrid):x_axis:=plot3d([u,0,0],u=0..2.5,v=0..0.01):y_axis:=plot3d([0,u,0],u=0..2.5,v=0..0.01):z_axis:=plot3d([0,0,u],u=0..2.5,v=0..0.01):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(pingmian,xyz,orientation=[40,60],lightmodel=light2,tickmarks=[4,4,4],title="XUXZJULY2009");第4页/共7页第四页，共8页。10.3三重积分

5with(plots):x1:=1:x2:=2:y1:=1:y2:=2:z1:=1:z2:=2:pingmian1:=plot3d([x,y,z1],x=x1..x2,y=y1..y2,color=blue):pingmian12:=plot3d([x,y,z2],x=x1..x2,y=y1..y2,color=blue):pingmian2:=plot3d([x,y1,z],x=x1..x2,z=z1..z2,color=yellow):pingmian22:=plot3d([x,y2,z],x=x1..x2,z=z1..z2,color=yellow):pingmian3:=plot3d([x1,y,z],y=y1..y2,z=z1..z2,color=green):pingmian32:=plot3d([x2,y,z],y=y1..y2,z=z1..z2,color=green):pingmian:=display({pingmian1,pingmian12,pingmian2,pingmian22,pingmian3,pingmian32},style=patchnogrid):Pingmian1:=plot3d([x,y,z1],x=x1-0.2..x2+0.2,y=0..y2+0.2,color=blue):Pingmian12:=plot3d([x,y,z2],x=x1-0.2..x2+0.2,y=0..y2+0.2,color=blue):Pingmian2:=plot3d([x,y1,z],x=0..x2+0.2,z=z1-0.2..z2+0.2,color=yellow):Pingmian22:=plot3d([x,y2,z],x=0..x2+0.2,z=z1-0.2..z2+0.2,color=yellow):Pingmian3:=plot3d([x1,y,z],y=y1-0.2..y2+0.2,z=0..z2+0.2,color=green):Pingmian32:=plot3d([x2,y,z],y=y1-0.2..y2+0.2,z=0..z2+0.2,color=green):Pingmian:=display({Pingmian1,Pingmian12,Pingmian2,Pingmian22,Pingmian3,Pingmian32},style=wireframe):x_axis:=plot3d([u,0,0],u=0..2.5,v=0..0.01):y_axis:=plot3d([0,u,0],u=0..2.5,v=0..0.01):z_axis:=plot3d([0,0,u],u=0..2.5,v=0..0.01):xyz:=display(x_axis,y_axis,z_axis,thickness=3):display(pingmian,Pingmian,xyz,orientation=[40,60],lightmodel=light2,tickmarks=[4,4,4],title="XUXZJULY2009");第5页/共7页第五页，共8页。10.3三重积分

6with(plots):x1:=1:x2:=2:y1:=1.2:y2:=2:z1:=0.8:z2:=1.6:pingmian1:=plot3d([x,y,z1],x=x1..x2,y=y1..y2,color=blue):pingmian12:=plot3d([x,y,z2],x=x1..x2,y=y1..y2,color=blue):pingmian2:=plot3d([x,y1,z],x=x1..x2,z=z1..z2,color=yellow):pingmian22:=plot3d([x,y2,z],x=x1..x2,z=z1..z2,color=yellow):pingmian3:=plot3d([x1,y,z],y=y1..y2,z=z1..z2,color=green):pingmian32:=plot3d([x2,y,z],y=y1..y2,z=z1..z2,color=green):pingmian:=display({pingmian1,pingmian12,pingmian2,pingmian22,pingmian3,pingmian32},style=patchnogrid):K:=60:forifrom1toKdoti:=i*360/K:A[i]:=display(pingmian,orientation=[ti,60])od:display(seq(A[i],i=1..K),insequence=true,title="XUXZJULY2009"