Mathematica Laboratory

The finalized Mathematica project is here. There are 4 parts. 2 numerical assignments and 2 creative parts.
Availability The Mathematica program can be obtained here. You can also Start here to register. After creating and validating your Wolfram account, sign in to the Wolfram User Portal and complete the Wolfram Activation Key Request Form. When selecting a product on the form, choose a version of "Mathematica for sites (single machine)." Click Submit. An activation key will be generated and emailed to you. Click the link for "Product Summary page". Click "Get Downloads" and select "Download" next to the appropriate platform. Follow the installation instructions and enter the activation key when prompted.
Running Mathematica Mathematica starts like any other application on OS X or Windows. On Linux, type "mathematica" in a terminal to start the notebook version, or "math" if you want to use the terminal version.
Some basic commands:
Plot[ x Sin[x],{x,-10,10}] Graph function of one variable
Plot3D[ Sin[x y],{x,-2,2},{y,-2,2}] Graph function of two variables
ParametricPlot[ {Cos[3 t],Sin[5 t]} ,{t,0,2Pi}] Plot planar curve
ParametricPlot3D[{Cos[t],Sin[t],t} ,{t,0,4Pi},AspectRatio->1] Plot space curve
ParametricPlot3D[{Cos[t] Sin[s],Sin[t] Sin[s],Cos[s]},{t,0,2Pi},{s,0,Pi}] Parametric Surface
SphericalPlot3D[(2+Sin[2 t] Sin[3 s]),{t,0,Pi},{s,0,2 Pi}] Spherical Plot
RevolutionPlot3D[{2 + Cos[t], t}, {t,0,2 Pi}] Revolution Plot
ContourPlot[Sin[x y],{x,-2,2},{y,-2,2} ] Contour lines (traces)
ContourPlot3D[x^2+2y^2-z^2,{x,-2,2},{y,-2,2},{z,-2,2}] Implicit surface
VectorPlot[{x-y,x+y},{x,-3,3},{y,-3,3}] Vectorfield plot
VectorPlot3D[{x-y,x+y,z},{x,-3,3},{y,-3,3},{z,0,1}] Vectorfield plot 3D
Integrate[x Sin[x], x] Integrate symbolically
Integrate[x y^2-z,{x,0,2},{y,0,x},{z,0,y}] 3D Integral
NIntegrate[Exp[-x^2],{x,0,10}] Integrate numerically
D[ Cos^5[x],x ] Differentiate symbolically
Series[Exp[x],{x,0,3} ] Taylor series
DSolve[ x''[t]==-x[t],x,t ] Solution to ODE
DSolve[{D[u[x,t],t]==D[u[x,t],x],u[x,0]==Sin[x]},u[x,t],{x,t}] Solution to PDE
Classify extrema:
ClassifyCriticalPoints[f_,{x_,y_}]:=Module[{X,P,H,g,d,S}, X={x,y}; 
P=Sort[Solve[Thread[D[f,#] & /@ X==0],X]]; H=Outer[D[f,#1,#2]&,X,X];g=H[[1,1]];d=Det[H];
S[d_,g_]:=If[d<0,"saddle",If[g>0,"minimum","maximum"]];
TableForm[{x,y,d,g,S[d,g],f} /.P,TableHeadings->{None,{x,y,"D","f_xx","Type","f"}}]]
ClassifyCriticalPoints[4 x y - x^3 y - x y^3,{x,y}]
Solve a Lagrange problem:
F[x_,y_]:=2x^2+4 x y;     G[x_,y_]:=x^2 y;
Solve[{D[F[x,y],x]==L*D[G[x,y],x],D[F[x,y],y]==L*D[G[x,y],y],G[x,y]==1},{x,y,L}]
Check that a function solves a PDE:
f[t_,x_]:=(x/t)*Sqrt[1/t]*Exp[-x^2/(4 t)]/(1+ Sqrt[1/t] Exp[-x^2/(4 t)]);
D[f[t,x],t]+f[t,x]*D[f[t,x],x]-D[f[t,x],{x,2}]
Simplify[%] Chop[%]