## Mathematica Laboratory

Availability The Mathematica program can be obtained here. The current version is Mathematica 8.04. During installation you will be prompted for an Activation Key. Students Faculty/Staff. Creation of a Wolfram account ID is optional. The contact information you provide must include your Harvard email address. Send me an email if you plan to use Mathematica on a linux system.
Getting the notebook This summer, we pioneer a Mathematica lab with 3D printing. You have templates, which can then be printed and bought.
• A Mathematica demo file can be obtained here.
• The assignment for Summer 2012 is here! Save this text file as "lab.nb" on your desktop and click on it.
Here are the 6 example objects given in the assignment.

## Project Hints

• Get inspired. If you use models you can find on the web like here, acknowledge the models, you use. More examples: something from the web
```A = Import["http://www.georgehart.com/rp/sierpinski5-george-hart.stl"];
B = Import["http://www.georgehart.com/rp/Goldberg-8-3-george-hart.stl"];
Show[Graphics3D[{Scale[A[[1]],2],Translate[Scale[B[[1]],0.6],{1,1,3}]}],Boxed->False]
```
Here is maybe a bit simpler example: "Kung Fu":
```A1 = {Blue, Cylinder[{{2, 1, 0}, {0, 3, 3}}, 0.1]};
A2 = {Red, Sphere[{2, 2, 2.5}, 0.6]};
A3 = {Orange, Cuboid[{1, 1, 1}, {2, 2, 2}]};
A4 = {Yellow, Sphere[{0, 3, 3}, 0.2]};
A4 = {Yellow, Sphere[{2, 1, 0}, 0.2]};
S = Show[Graphics3D[Scale[{A1, A2, A3, A4, A5}, 0.2]],
Axes -> True, PlotRange -> All, ViewPoint -> {0.51, 3.30, 0.494},
ViewVertical -> {0.11, 0.680, 0.76}]
```
. A list of Polyhedra can be obtained from
```PolyhedronData[]
```
Choose one and see it with
```PolyhedronData["GyroelongatedPentagonalRotunda"]
```
• Check out the photos of the printed models.

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};
```F[x_,y_]:=2x^2+4 x y;     G[x_,y_]:=x^2 y;
```f[t_,x_]:=(x/t)*Sqrt[1/t]*Exp[-x^2/(4 t)]/(1+ Sqrt[1/t] Exp[-x^2/(4 t)]);