SetDirectory["C:\\Documents and Settings\\alpha\\My Documents\\Teaching\\Partial Differential Equations\\Lectures"]

$TextStyle={FontFamily->"Times",FontSize->14}

field=VectorPlot[{-y,x},{x,-2,2},{y,-2,2},VectorScale->{Tiny,Tiny,None},FrameLabel->{"x","y"}] 
Export["figCha1.jpg",%,"JPEG"]

solplot = ContourPlot[{x^2+ y^2==0,x^2+ y^2==1,x^2+ y^2==2,x^2+ y^2==3,x^2+ y^2==4,x^2+ y^2==6,x^2+ y^2==8,x^2+ y^2==10},{x,-2,2},{y,-2,2},ContourStyle->Thick]

Show[field,solplot]
Export["figCha2.jpg",%,"JPEG"]

CC =x^2+y^2

f[x_] = x
Plot3D[f[CC],{x,-2,2},{y,-2,2},PlotPoints->40,AxesLabel->{"x","y","z"}]
Export["figCha31a.jpg",%,"JPEG"]
ContourPlot[f[CC],{x,-2,2},{y,-2,2},PlotPoints->40,ContourShading->False,FrameLabel->{"x","y"}]
Export["figCha31b.jpg",%,"JPEG"]

f[x_] = -x
Plot3D[f[CC],{x,-2,2},{y,-2,2},PlotPoints->40,AxesLabel->{"x","y","z"}]
Export["figCha32a.jpg",%,"JPEG"]
ContourPlot[f[CC],{x,-2,2},{y,-2,2},PlotPoints->40,ContourShading->False,FrameLabel->{"x","y"}]
Export["figCha32b.jpg",%,"JPEG"]

f[x_] = Cos[Sin[x]]
Plot3D[f[CC],{x,-2,2},{y,-2,2},PlotPoints->40,AxesLabel->{"x","y","z"}]
Export["figCha33a.jpg",%,"JPEG"]
ContourPlot[f[CC],{x,-2,2},{y,-2,2},PlotPoints->40,ContourShading->False,FrameLabel->{"x","y"}]
Export["figCha33b.jpg",%,"JPEG"]

f[x_] = Exp[-x^2]Cos[x] -x*Sin[x] +x
Plot3D[f[CC],{x,-2,2},{y,-2,2},PlotPoints->40,AxesLabel->{"x","y","z"}]
Export["figCha34a.jpg",%,"JPEG"]
ContourPlot[f[CC],{x,-2,2},{y,-2,2},PlotPoints->80,ContourShading->False,FrameLabel->{"x","y"}]
Export["figCha34b.jpg",%,"JPEG"]

surf2 = ParametricPlot3D[{s,w,Cos[s^2+w^2]},{s,-2,2},{w,-2,2},ViewPoint->{10,5,10},AxesLabel->{"x","y","z"},PlotPoints->30]
Export["figCha4a.jpg",%,"JPEG"]

plane = ParametricPlot3D[{-0.1,s,w},{s,-3,3},{w,-1,1},ViewPoint->{10,5,10},AxesLabel->{"x","y","z"}]

surf2 = ParametricPlot3D[{s,w,Cos[s^2+w^2]},{s,-2,0},{w,-3,3},ViewPoint->{10,5,10},AxesLabel->{"x","y","z"},PlotPoints->40,ColorFunction->"BlueGreenYellow"]

Show[surf2,plane,ViewPoint->{5,2,5}]
Export["figCha4b.jpg",%,"JPEG"]

Plot[Cos[y^2],{y,-3,3},AxesLabel->{"y","z"}]
Export["figCha4c.jpg",%,"JPEG"]