Mathematica Laboratory

The Mathematica project is due on July 29, 2017, stamp of the email.

here.

Availability The Mathematica program can be obtained here. Start there, rather than at the Wolfram User portal. You will be directed there to 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. The current version is Mathematica 10. During installation you will be prompted for an Activation Key. Send me an email if you plan to use Mathematica on a linux system.
Getting the notebook Here is the Mathematica file authored during the workshop.
  • Major points about the project:
    • Be creative. Acknowledge any sources used. In doubt, check with Oliver.
    • Each one submits an individual project. Checking with each other is fine. But each should have something original.
    • The deadline is strict. The email should have the date of Saturday or earlier. A project arriving with a July 30 date does not qualify.
    • Submit the Mathematica .nb file, ONE file. If possible, call the file with your name. If the graphics is too large, remove the graphics first before emailing it in. I need the Mathematica code however.
    • Save the project regularily. Also versions. Work so that you have a reasonable project at all time, then push it as far as you can.
  • 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[%]