工科高数下册实验课第一讲

工科高等数学下册实验东北农业大学信息与计算科学系实验课安排实验二：多元函数微分学实验一：空间曲面与曲线的图形实验三：重积分、曲线积分和曲面积分实验一2.绘制空间曲面在坐标面上的投影。1.运用Mathematica语句绘制空间曲面和空间曲线的图形。空间曲面图形的绘格式Plot[f[x],{x,xmin,xmax},可选项]二元函数绘图命令复习：一元函数的绘图命令Plot3D[f[x,y],{x,xmin,xmax},{y,ymin,ymax},可选项]格式例1画出函数22yxz22yxz22yxz22yxz22yxz22yxz22yxz22yxz22yxz的图形。In[]:=Plot3D[x^2+y^2,{x,-5,5},{y,-5,5}]-4-2024-4-202402040-4-2024常用可选项22yxz22yxz22yxz22yxz22yxz22yxz22yxz22yxzIn[]:=Plot3D[x^2+y^2,{x,-5,5},{y,-5,5},Axes→False]In[]:=Plot3D[x^2+y^2,{x,-5,5},{y,-5,5},Boxed→False]-4-2024-4-202402040-4-2024In[]:=Plot3D[x^2+y^2,{x,-5,5},{y,-5,5},Mesh→False]-4-2024-4-202402040-4-2024In[]:=Plot3D[x^2+y^2,{x,-5,5},{y,-5,5},PlotPoints→25]-4-2024-4-202402040-4-2024In[]:=Plot3D[x^2+y^2,{x,-5,5},{y,-5,5},Shading→False]-4-2024-4-202402040-4-2024In[]:=Plot3D[x^2+y^2,{x,-5,5},{y,-5,5},ViewPoint→{-1.632，-2.569，1.479}]-4-2024-4-202402040-4-2024-4-2024空间曲面的参数方程绘图格式ParametricPlot3D[{x(u,v),y(u,v),z(u,v)},{u,umin,umax},{v,vmin,vmax},可选项]例2画出椭圆抛物9422yxz的图形。x=2usinv,y=3ucosv,z=u^2(0In[]:=ParametricPlot3D[{2u*Sin[v],3u*Cos[v],u^2}，{u,0,5},{v,0,2Pi}]u5,0v)2-10-50510-1001001020-10-50510-10010空间曲线的参数方程绘图格式ParametricPlot3D[{x(t),y(t),z(t)},{t,tmin,tmax},可选项]例3绘出曲线2/cos2sintztytx的图形。In[]:=ParametricPlot3D[{Sin[t],2Cos[t],t/2},{t,0,20}]-1-0.500.51-2-101202.557.510-2-1012空间曲面在坐标面上的投影1.在YOZ面上的投影，将x设为常数aParametricPlot3D[{a,y(u,v),z(u,v)},{u,umin,umax},{v,vmin,vmax},可选项]2.在ZOX面上的投影，将y设为常数bParametricPlot3D[{x(u,v),b,z(u,v)},{u,umin,umax},{v,vmin,vmax},可选项]3.在XOY面上的投影，将z设为常数cParametricPlot3D[{x(u,v),y(u,v),c},{u,umin,umax},{v,vmin,vmax},可选项]例4观察椭圆抛物面9422yxz在各坐标面上的投影。In[]:=a=ParametricPlot3D[{2u*Sin[v],3u*Cos[v],u^2},{u,0,5},{v,0,2Pi}]In[]:=b=ParametricPlot3D[{2u*Sin[v],3u*Cos[v],0},{u,0,5},{v,0,2Pi}]-10-50510-10010-1-0.500.51-10-50510-10-50510-1001001020-10-50510-10010-10-50510-1001001020-10-50510-10010In[]:=Show[a,b]综合练习例5画出双曲抛物面6922yxz被平面图形。0zIn[]:=c=Plot3D[x^2/9-y^2/6,{x,-2,2},{y,-2,2}]In[]:=d=Plot3D[0,{x,-2,2},{y,-2,2}]-2-1012-2-1012-1-0.500.51-2-1012-2-1012-2-1012-0.5-0.2500.25-2-1012所截的In[]:=Show[c,d]-2-1012-2-1012-0.200.2-2-1012例6绘出空间直角坐标系。In[]:=e=ParametricPlot3D[{u,v,0},{u,-2,2},{v,-2,2}]In[]:=f=ParametricPlot3D[{0,u,v},{u,-2,2},{v,-2,2}]In[]:=g=ParametricPlot3D[{u,0,v},{u,-2,2},{v,-2,2}]-2-1012-2-1012-1-0.500.51-2-1012-1-0.500.51-2-1012-2-1012-1-0.500.51-2-1012-2-1012-1-0.500.51-2-1012-1-0.500.51-2-1012In[]:=Show[e,f,g]-2-1012-2-1012-2-1012-2-1012-2-1012例7作部分球面。43球面。1.画出In[]:=d1=ParametricPlot3D[{Sin[u]*Cos[v],Sin[u]*Sin[v],Cos[u]},{u,0,Pi},{v,0,3Pi/2}]In[]:=d2=ParametricPlot3D[{Sin[u]*Cos[v],Sin[u]*Sin[v],Cos[u]},{u,Pi/4,Pi},{v,0,2Pi}]-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.5-1-0.500.51-1-0.500.512.画出上半球面的43部分。In[]:=ParametricPlot3D[{Sin[u]*Cos[v],Sin[u]*Sin[v],Cos[u]},{u,0,Pi/2},{v,0,3Pi/2}]-1-0.500.51-1-0.500.5100.250.50.751-1-0.500.513.小球面与43大球面的叠加。In[]:=d3=ParametricPlot3D[{Sin[u]*Cos[v]/2,Sin[u]*Sin[v]/2,Cos[u]/2},{u,0,Pi},{v,0,2Pi}]-0.5-0.2500.250.5-0.5-0.2500.250.5-0.5-0.2500.250.5-0.5-0.2500.250.5-0.5-0.2500.250.5In[]:=Show[d1,d3]-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51-1-0.500.51In[]:=Show[d2,d3,ViewPoint→{0.088,0.264,3.372}]-1-0.500.51-1-0.500.51-1-0.500.5-1-0.500.51