MATH 126: 3D surfaces

Worksheet problem 1

ContourPlot3D[y==2,{x,-5,5},{y,-5,5},{z,-5,5},AxesLabel->Automatic]

ContourPlot3D[x^2+y^2==1,{x,-1,1},{y,-1,1},{z,-1,1},AxesLabel->Automatic]

Worksheet problem 2: f(x,y)=(Sqrt[(x^2)-(y^2)])

Plot3D[Sqrt[(x^2)-(y^2)],{x,-4,4},{y,-4,4},AxesLabel->Automatic]

Worksheet problem 6

Cone: z=(Sqrt[((x^2)/2)+((y^2)/2)])

GraphicsRow[{
Plot3D[(Sqrt[(x^2)+(y^2)]),{x,y}∈Disk[{0,0},2],PlotRange->{0,2},BoxRatios->{1,1,1}],
ContourPlot[(Sqrt[(x^2)+(y^2)]),{x,y}∈Disk[{0,0},2],Contours->16,ContourShading->None,PlotRange->All,FrameLabel->Automatic]
}]

Manipulate[Show[
Plot3D[(Sqrt[(x^2)+(y^2)]),{x,y}∈Disk[{0,0},2],PlotRange->{0,2},BoxRatios->{1,1,1}],Plot3D[h,{x,-2,2},{y,-2,2},ColorFunction->Blue]],
{h,0,2}]

Paraboloid: z=((x^2)/2)+((y^2)/2)

GraphicsRow[{
Plot3D[((x^2)/2)+((y^2)/2),{x,-2,2},{y,-2,2},AxesLabel->Automatic,BoxRatios->Automatic],
ContourPlot[((x^2)/2)+((y^2)/2),{x,-4,4},{y,-4,4},Contours->16,ContourShading->None,PlotRange->All,FrameLabel->Automatic]
}]

Manipulate[Plot3D[{((x^2)/2)+((y^2)/2),h},{x,-2,2},{y,-2,2},AxesLabel->Automatic,PlotRange->All,BoxRatios->Automatic],{h,-2,2}]

Hyperbolic Paraboloid: z=((x^2)/2)-((y^2)/2)

GraphicsRow[{
Plot3D[((x^2)/2)-((y^2)/2),{x,-2,2},{y,-2,2},AxesLabel->Automatic,BoxRatios->Automatic],
ContourPlot[((x^2)/2)-((y^2)/2),{x,-4,4},{y,-4,4},Contours->16,ContourShading->None,PlotRange->All,FrameLabel->Automatic]
}]

Manipulate[Plot3D[{((x^2)/2)-((y^2)/2),h},{x,-2,2},{y,-2,2},AxesLabel->Automatic,PlotRange->All,BoxRatios->Automatic],{h,-2,2}]

Worksheet problem 7

GraphicsRow[{
Plot3D[-3x Exp[-(x^2)-(y^2)],{x,-3,3},{y,-3,3},AxesLabel->Automatic,BoxRatios->Automatic,PlotRange->{-1.5,1.5}],
ContourPlot[-3x Exp[-(x^2)-(y^2)],{x,-3,3},{y,-3,3},Contours->17,ContourShading->None,PlotRange->All,FrameLabel->Automatic]
}]

Manipulate[Plot3D[{-3x Exp[-(x^2)-(y^2)],h},{x,-3,3},{y,-3,3},AxesLabel->Automatic,BoxRatios->Automatic,PlotRange->{-2,2}],{h,-2,2}]