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1、高数实验报告李峰灯042097151.利用参数方程作图,作出由下列曲面所围成的立体<1)z=1-x^2-y^2,x^2+y^2=x,z=0t1=ParametricPlot3D[{Cos[u]*Sin[v],Sin[u]*Sin[v],Cos[v]},{u,0,2*p},{v,0,p/2},AxesLabel®{"X","Y","Z"},DisplayFunction®Identity]。b5E2RGbCAPt2=ParametricPlot3D[{Cos[u]*0.5+0.5,0.5*Sin[u],v},{u,0,2*p},{v,0,
2、1},AxesLabel®{"X","Y","Z"},DisplayFunction®Identity]。p1EanqFDPwt3=ParametricPlot3D[{u,v,0},{u,-1,1},{v,-1,1},AxesLabel®{"X","Y","Z"},DisplayFunction®Identity]。DXDiTa9E3dShow[t1,t2,t3,DisplayFunction®$DisplayFunction]<2)z=x*y,x+y-1=0及z=0t1=ParametricPlot3D[{u,v,u*v},{u,0,
3、1},{v,-1,1},AxesLabel®{"X","Y","Z"},DisplayFunction®Identity]。RTCrpUDGiTt2=ParametricPlot3D[{u,1-u,v},{u,-1,1},{v,-1,1},AxesLabel®{"X","Y","Z"},DisplayFunction®Identity]。5PCzVD7HxAt3=ParametricPlot3D[{u,v,0},{u,-1,1},{v,-1,1},AxesLabel®{"X","Y","Z"},DisplayFunction®Ident
4、ity]。jLBHrnAILgShow[t1,t2,t3,DisplayFunction®$DisplayFunction]xHAQX74J0X5/52.观察函数展成的Fourier级数的部分和逼近的情况。因为,=dx=+1,且故输入以下命令,从输出的图形观察Fourier级数的部分和逼近的情况:5/55/5从图中可以看出,n越大逼近函数的效果越好,并且还可以注意到Fourier级数的逼近是整体性的。3.一种合金在某种添加剂的不同浓度下进行实验,得到如下数据:浓度x10.015.020.025.030.0抗压强度y27.026.826.
5、526.326.1已知函数y与x的关系适合模型:,试用最小二乘法确定系数a,b,c,并求出拟合曲线。解:x={10.0,15.0,20.0,25.0,30.0}。y={27.0,26.8,26.5,26.3,26.1}。m=x^2。n=x。z=y。mnz=Table[{m[[i]],n[[i]],z[[i]]},{i,1,5}]。q[a_,b_,c_]:=Sum[(c*m[[i]]+b*n[[i]]+a-z[[i]]>^2,{i,1,5}]LDAYtRyKfESolve[{D[q[a,b,c],a]0,D[q[a,b,c],b]0,D[
6、q[a,b,c],c]0},{a,b,c}]5/5Zzz6ZB2LtkA={a,b,c}/.%。a=A[[1,1]]b=A[[1,2]]c=A[[1,3]]data=Table[{x[[i]],y[[i]]},{i,1,5}]。t1=ListPlot[data,PlotStyle®PointSize[0.02],DisplayFunction®Identity]。dvzfvkwMI1f[x_]:=a+b*x+c*x^2。t2=Plot[f[x],{x,5.0,200},AxesOrigin®{5.0,0},DisplayFunction
7、®Identity]。Show[t1,t2,DisplayFunction®$DisplayFunction]运行后得到结果为:a=b=c=拟合曲线为:申明:所有资料为本人收集整理,仅限个人学习使用,勿做商业用途。5/5