1、,三重積分的概念與計(jì)算,2013.4.15,1,PPT學(xué)習(xí)交流,2,PPT學(xué)習(xí)交流,3,PPT學(xué)習(xí)交流,with(plots):a:=(sqrt(5)-1)/2: u:=(x,y)-sqrt(x2+y2): v:=(x,y)-1-x2-y2: qumian1:=plot3d(u(x,y),x=-a.a,y=-sqrt(a2-x2).sqrt(a2-x2),color=yellow): qumian2:=plot3d(v(x,y),x=-a.a,y=-sqrt(a2-x2).sqrt(a2-x2),color=green): quxian:=spacecurve(a*cos(t),a*sin(t

2、),u(a*cos(t),a*sin(t),t=0.2*Pi,color=red,thickness=4): x_axis:=plot3d(u,0,0,u=-1/2.1/2,v=0.0.01,thickness=3): y_axis:=plot3d(0,u,0,u=-1/2.1/2,v=0.0.01,thickness=3): z_axis:=plot3d(0,0,u,u=-.2.1.2,v=0.0.01,thickness=3): xyz:=display(x_axis,y_axis,z_axis,thickness=3): display(qumian1,qumian2,quxian,xy

3、z,scaling=constrained,orientation=20,60);,4,PPT學(xué)習(xí)交流,with(plots):R:=(sqrt(5)-1)/2: qumian1:=plot3d(s*cos(t),s*sin(t),s,t=0.2*Pi,s=0.R,color=yellow): qumian2:=plot3d(s*cos(t),s*sin(t),1-s2,t=0.2*Pi,s=0.R,color=green): x_axis:=plot3d(u,0,0,u=-1/2.1/2,v=0.0.01,thickness=3): y_axis:=plot3d(0,u,0,u=-1/2.1

4、/2,v=0.0.01,thickness=3): z_axis:=plot3d(0,0,u,u=-.2.1.2,v=0.0.01,thickness=3): xyz:=display(x_axis,y_axis,z_axis,thickness=3): display(qumian1,qumian2,xyz,scaling=constrained,orientation=33,68),5,PPT學(xué)習(xí)交流,6,PPT學(xué)習(xí)交流,7,PPT學(xué)習(xí)交流,f:=(x,y,z)-y*cos(x+z): x1:=0:x2:=Pi/2: y1:=x-0:y2:=x-sqrt(x): z1:=(x,y)-0:z

5、2:=(x,y)-Pi/2-x: Int(Int(Int(f(x,y,z),z=z1(z,y).z2(z,y),y=y1(x).y2(x),x=x1.x2) =int(int(int(f(x,y,z),z=z1(x,y).z2(x,y),y=y1(x).y2(x),x=x1.x2);,8,PPT學(xué)習(xí)交流,9,PPT學(xué)習(xí)交流,with(plots): qumian1:=plot3d(x,0,z,x=0.Pi/2,z=0.Pi/2-x,color=yellow): qumian2:=plot3d(x,y,0,x=0.Pi/2,y=0.sqrt(x),color=green): qumian3:=p

6、lot3d(x,sqrt(x),z,x=0.Pi/2,z=0.Pi/2-x,color=brown): qumian4:=plot3d(x,y,Pi/2-x,x=0.Pi/2,y=0.sqrt(x),color=gray): x_axis:=plot3d(u,0,0,u=-1/2.2,v=0.0.01,thickness=3): y_axis:=plot3d(0,u,0,u=-1/2.1,v=0.0.01,thickness=3): z_axis:=plot3d(0,0,u,u=-.2.2,v=0.0.01,thickness=3): xyz:=display(x_axis,y_axis,z_

7、axis,thickness=3): display(qumian1,qumian2,qumian3,qumian4,xyz,scaling=constrained,orientation=55,68);,10,PPT學(xué)習(xí)交流,11,PPT學(xué)習(xí)交流,f:=(x,y,z)-x*z/(1+y)2: x1:=0:x2:=1: y1:=x-x2:y2:=x-1: z1:=(x,y)-0:z2:=(x,y)-1-y2: Int(Int(Int(f(x,y,z),z=z1(z,y).z2(z,y),y=y1(x).y2(x),x=x1.x2) =int(int(int(f(x,y,z),z=z1(x,y)

8、.z2(x,y),y=y1(x).y2(x),x=x1.x2);,12,PPT學(xué)習(xí)交流,13,PPT學(xué)習(xí)交流,with(plots): qumian1:=plot3d(0,y,z,y=0.1,z=0.1-y2,color=yellow): qumian2:=plot3d(x,y,0,x=0.1,y=x2.1,color=green): qumian3:=plot3d(x,x2,z,x=0.1,z=0.1-x4,color=brown): qumian4:=plot3d(x,y,1-y2,x=0.1,y=x2.1,color=gray): x_axis:=plot3d(u,0,0,u=-1/2.

9、1,v=0.0.01,thickness=3): y_axis:=plot3d(0,u,0,u=-1/2.1.5,v=0.0.01,thickness=3): z_axis:=plot3d(0,0,u,u=-.2.1.5,v=0.0.01,thickness=3): xyz:=display(x_axis,y_axis,z_axis,thickness=3): display(qumian1,qumian2,qumian3,qumian4,xyz,scaling=constrained,orientation=55,68);,14,PPT學(xué)習(xí)交流,15,PPT學(xué)習(xí)交流,f:=(x,y,z)-e

10、xp(abs(z); theta1:=0:theta2:=2*Pi: r1:=theta-0:r2:=theta-sqrt(1-z2): z1:=(x,y)-1:z2:=(x,y)-1: Int(Int(Int(f(x,y,z)*r,r=r1(theta).r2(theta),theta=theta1.theta2),z=z1.z2) =int(int(int(f(x,y,z)*r,r=r1(theta).r2(theta),theta=theta1.theta2),z=z1.z2);,16,PPT學(xué)習(xí)交流,17,PPT學(xué)習(xí)交流,f:=(x,y,z)-x: x1:=0:x2:=1: y1:=x

11、-0:y2:=x-(1-x)/(1+x): z1:=(x,y)-0:z2:=(x,y)-x*y: Int(Int(Int(f(x,y,z),z=z1(z,y).z2(z,y),y=y1(x).y2(x),x=x1.x2) =int(int(int(f(x,y,z),z=z1(x,y).z2(x,y),y=y1(x).y2(x),x=x1.x2);,f:=(x,y,z)-x: x1:=0:x2:=1: y1:=x-(1-x)/(1+x):y2:=x-1-x: z1:=(x,y)-0:z2:=(x,y)-1-x-y: Int(Int(Int(f(x,y,z),z=z1(z,y).z2(z,y),y

12、=y1(x).y2(x),x=x1.x2) =int(int(int(f(x,y,z),z=z1(x,y).z2(x,y),y=y1(x).y2(x),x=x1.x2);,18,PPT學(xué)習(xí)交流,with(plots): pingmian1:=implicitplot3d(z=0,x=-.2.1.2,y=-0.2.1.2,z=-1.1,color=grey,style=patchnogrid): pingmian2:=implicitplot3d(z=1-x-y,x=-.2.1.2,y=-0.2.1.2,z=-0.5.1.2,color=green,style=patchnogrid): qum

13、ian:=implicitplot3d(z=x*y,x=-.2.1.2,y=-0.2.1.2,z=-1.1.3,color=brown,style=patch): x_axis:=plot3d(u,0,0,u=-1.1.3,v=0.0.01,thickness=3): y_axis:=plot3d(0,u,0,u=-1.1.5,v=0.0.01,thickness=3): z_axis:=plot3d(0,0,u,u=-.3.1.5,v=0.0.01,thickness=3): xyz:=display(x_axis,y_axis,z_axis,thickness=3): text:=text

14、plot3d(0,0,-.8,SCUMATH 2008,color=grey): display(qumian,pingmian1,pingmian2,text,xyz,scaling=constrained);,以下曲面所圍成的立體：,19,PPT學(xué)習(xí)交流,20,PPT學(xué)習(xí)交流,在D1上：,在D2上：,21,PPT學(xué)習(xí)交流,with(plots): pingmian1:=plot3d(x,y,0,x=0.1,y=0.1-x,color=grey,style=patchnogrid): pingmian2:=plot3d(x,y,1-x-y,x=0.1,y=(1-x)/(1+x).1-x,co

15、lor=green,style=patchnogrid): qumian:=plot3d(x,y,x*y,x=0.1,y=0.(1-x)/(1+x),color=brown,style=patchnogrid): x_axis:=plot3d(u,0,0,u=-.1.1.1,v=0.0.01,thickness=3): y_axis:=plot3d(0,u,0,u=-.1.1.1,v=0.0.01,thickness=3): z_axis:=plot3d(0,0,u,u=-.1.0.2,v=0.0.01,thickness=3): xyz:=display(x_axis,y_axis,z_ax

16、is,thickness=3): display(qumian,pingmian1,pingmian2,xyz,scaling=constrained);,22,PPT學(xué)習(xí)交流, with(plots): pingmian:=plot3d(x,y,0,x=0.1,y=0.1-x,color=grey,style=patchnogrid): qumian2:=plot3d(x,(1-x)/(1+x),z,x=0.1,z=0.x*(1-x)/(1+x),color=gold,style=patchnogrid): qumian:=plot3d(x,y,x*y,x=0.1,y=0.(1-x)/(1+x),color=brown,style=patchnogrid): x_axis:=plot3d(u,0,0,u=-.1