实验4作出函数∫(xy)=e()的等高线和梯度线的图形,并观察梯度线 与等高线的关系 程序 fxy}=E^(-(x^2+2y^2)/10~4)Plo3D[1xy],{x-1.2,1,2},{y-1.2,1.2} t1=ContourPlotfx, y](x,-1.2, 1.2),y-1.2, 1. 2), Plot Points->50 Contour Shading->False] fx[x_y]=Evaluate[D[f[x, yl, x]]; fy[x_,y_=Evaluate[D[f(x,yl, yl X0=1.0 y0=1.0; lamda=0.01; a=x0; b-yo Dolu=atlamda *fx[a, b/Sqrt[(fx[a, b]2+(fyla, b] 2 v=b+lamda*fy[a,b/Sqrt[(fx[a, b]2+(fyla,b ]2 c[n]=ud[n]=v;a=u;b=v,{n,200} data=Table[cn], d[n,n, 200] t2=ListPlot[ data, PlotJoined->True, PlotStyle->RGBColor[1,0,011 Showltl, t2, AspectRatio->Automatic, PlotRange->All <<Calculus Vector Analysis <<Graphics PlotField SetCoordinates[Cartesian[x, y, z; uE((x2+2y/)/10 4) complot=Show[tl, Display Function->Identity gradplot=Show[t2, Display Function->Identity] t-PlotGradient Fieldu, x,-1. 2, 1.2,y-1. 2, 1. 2), Display Function->Identity ] Show[complot, gradplot, t, Display Function->DIsplay Function] 结果实验4 作出函数 的等高线和梯度线的图形，并观察梯度线 与等高线的关系 程序： f[x_,y_]=E^(-(x^2+2y^2)/10^4);Plot3D[f[x,y],{x,-1.2,1.2},{y,-1.2,1.2}]; t1=ContourPlot[f[x,y],{x,-1.2,1.2},{y,-1.2,1.2},PlotPoints->50, ContourShading->False]; fx[x_,y_]=Evaluate[D[f[x,y],x]];fy[x_,y_]=Evaluate[D[f[x,y],y]]; x0=1.0;y0=1.0;lamda=0.01;a=x0;b=y0; Do[u=a+lamda*fx[a,b]/Sqrt[(fx[a,b])^2+(fy[a,b])^2]; v=b+lamda*fy[a,b]/Sqrt[(fx[a,b])^2+(fy[a,b])^2]; c[n]=u;d[n]=v;a=u;b=v,{n,200}] data=Table[{c[n],d[n]},{n,200}]; t2=ListPlot[data,PlotJoined->True,PlotStyle->RGBColor[1,0,0]]; Show[t1,t2,AspectRatio->Automatic,PlotRange->All]; <<Calculus`VectorAnalysis` <<Graphics`PlotField` SetCoordinates[Cartesian[x,y,z]];u=E^(-(x^2+2y^2)/10^4); conplot=Show[t1,DisplayFunction->Identity]; gradplot=Show[t2,DisplayFunction->Identity]; t=PlotGradientField[u,{x,-1.2,1.2},{y,-1.2,1.2},DisplayFunction->Identity]; Show[conplot,gradplot,t,DisplayFunction->$DisplayFunction]; 结果：