15.1 Functions of Several Variables

Plot3D[
      Sin[(Sqrt[(x^2) + (y^2)])], {x, -2 π, 2  π}, {y, -2 π, 
        2  π},  PlotPoints -> 50]

ContourPlot[
      Sin[(Sqrt[(x^2) + (y^2)])], {x, -2 π, 2  π}, {y, -2 π, 
        2  π}, ContourShading -> False, 
      PlotPoints -> 50]

Plot3D[(1/((x^2) + 4  (y^2))), {x, -3, 3}, {y, -3, 3},  
      PlotRange -> {0, 20}, BoxRatios -> Automatic, 
      PlotPoints -> 50]

ContourPlot[(1/((x^2) + 4  (y^2))), {x, -3, 3}, {y, -3, 3}, 
      ContourShading -> False,  PlotPoints -> 50]

Plot3D[
      Sin[x] Sin[y], {x, -2 π, 2  π}, {y, -2 π, 
        2  π},  PlotPoints -> 50]

ContourPlot[
      Sin[x] Sin[y], {x, -2 π, 2  π}, {y, -2 π, 
        2  π}, ContourShading -> False, 
      PlotPoints -> 50]

Plot3D[(x^2) (y^2) (E^(-(x^2) - (y^2))), {x, -4, 
        4}, {y, -4, 4},  PlotRange -> {0,  .2}, 
      PlotPoints -> 50]

ContourPlot[(x^2) (y^2) (E^(-(x^2) - (y^2))), {x, -4, 
        4}, {y, -4, 4}, ContourShading -> False, 
      PlotPoints -> 50]

Plot3D[(x^3) - 3  x (y^2), {x, -1, 1}, {y, -1, 1}, 
      BoxRatios -> Automatic,  PlotPoints -> 50]

ContourPlot[(x^3) - 3  x (y^2), {x, -1, 1}, {y, -1, 1}, 
      ContourShading -> False, PlotPoints -> 50]

Plot3D[
      Sin[x]^2 + (1/4) (y^2), {x, -2 π, 2  π}, {y, -4, 
        4},  PlotPoints -> 50]

ContourPlot[
      Sin[x]^2 + (1/4) (y^2), {x, -2 π, 2  π}, {y, -4, 4}, 
      ContourShading -> False, PlotPoints -> 50]