PLOTTING USING MATHEMATICA                  2 - d Plotting

Plotting y = f (x) for f (x) = x^2

Plot[x^2, {x, -1, 1}]

Parametric plot of curve x = t^2,  y = t

ParametricPlot[{t^2, t}, {t, -3, 2}]

Polar coordinates You must always execute the following in order to graph		in polar coordinates

Needs["Graphics`Graphics`"];

\(Here\ t\ \ is\ used\ in\ place\ of\ theta\ and\ the\ first\ argument\ 
        of

      Polarplot\ is\ r\ as\ a\ function\ of\ t . \ The\ following\ gives\ the
        \ polar

      graph\ of\ \ r = t^2. \)

PolarPlot[t^2, {t, -2*Pi, 2 * Pi}]

3 - d Plotting

Surfaces specified by z = f (x, y)Here f (x, y) = x^2 + y^4

Plot3D[x^2 + y^4, {x, -30, 30}, {y, -6, 6}]

\(Contour\ \ plots\ of\ functions\ \ of\ two\ 

      variables : level\ curves\ in\ x - y\ plane\)

ContourPlot[Sin[x*y],  {x, 0, 3},  {y, 0, 3}]

Plotting parametric curves in 3 - d

ParametricPlot3D[{t, t*Cos[t],  Sin[t]},  {t,  -2, 2} ]

Plotting implicitly defined functions in 3 - dYou need to execute the following command in order to be 
        able to plot implicit functions in 3 d .

Needs["Graphics`ContourPlot3D`"]

\(\(ContourPlot3D[
      x^2 + y^2 + z^2 - 1, {x, \(-1\), 1}, {y, \(-1\), 1}, {z, \(-1\), 1}]

    \)\)

Plotting in cylindrical and spherical coordinatesYou need to execute the following command in order to plot 
        in cylindrical or spherical coordinates

Needs["Graphics`ParametricPlot3D`"];

Cylindrical coordinate plot --  CylindricalPlot3D The first argument is z, the second is r and the third is t (theta)

CylindricalPlot3D[r^2  Sin[2  t],  {r, 0, 1}, {t,  0,  2 Pi}]

Spherical coordinate plot -- SphericalPlot3D The first argument is r,  
        the second is psi (angle from z axis),  
        and the third is theta 
          (angle from x axis in xy plane) .

SphericalPlot3D[2 + Sin[2  t] Sin[3  p], {t,  0,  Pi}, 
       {p, 0, 2  Pi}]