Mathematica Laboratory
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Deadline The Mathematica project is due the last day of class.
That is Friday May 5'th for the Mo/We/Fr sections, and Tuesday May
4'th for the Tue/Thu sections. You hand in the Mathematica project
printout with the last homework. We need a physical printout which
contains the graphics and answers to the questions at the end of the
notebook. Show your work. Also for the graphics plots, we need to
see the command, which produced the plot.
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| Availability |
Mathematica is installed on some computers in the basement of the Science center.
It might also be installed on some computers in the houses. If you want to try
an installation of Mathematica on your own computer,
get it here.
Note that you have to be on a Harvard network and have your PIN ready to download the
software and that requesting the Mathematica Password requires you to send the
request from a Harvard computer.
| | Installation |
After you downloaded the program to your computer, start the application and follow
the instructions. During the installation progress, you have to enter the
Harvard Licence number L2482-2405. The number which you will get in return has
to be entered in the Mathematica Registration page. You will then be sent a
password by email. This is what you see during installation in
Send email to math21a@fas, if you plan to use Mathematica on a linux system.
| | Getting the notebook |
- The Mathematica laboratory assignment will be posted
You can see a HTML preview of the lab here.
| | Running mathematica |
Mathematica is started like any other application on Macintoshs or PC's.
On Linux, just type "mathematica" to start the notebook version, or
"math" to start the terminal version.
| | Some frequently used commands:
( See more what you can do with
Mathematica) |
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Example how to check homework: change the function and get an analysis about its critical points:
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(* Mathematica code to classify critical points, O. knill, 2000 *)
f[x_,y_]:=4 x y - x^3 y - x y^3;
a[x_,y_]:=D[f[u,v],u] /. {u->x,v->y}; b[x_,y_]:=D[f[u,v],v] /. {u->x,v->y};
A=Solve[{a[x,y]==0,b[x,y]==0},{x,y}];
CriticalPoints=Table[{A[[i,1,2]],A[[i,2,2]]},{i,Length[A]}];
H[{x_,y_}]:={{D[f[u,v],{u,2}],D[D[f[u,v],v],u]},{D[D[f[u,v],u],v],D[f[u,v],{v,2}]}} /. {u->x,v->y};
F[A_]:=A[[1,1]]; Discriminant=Map[Det,Map[H,CriticalPoints]]
FirstEntry=Map[F,Map[H,CriticalPoints]]
Decide[B_]:=If[Det[B]<0,"saddle",If[B[[1,1]]<0,"max","min"]];
Analysis=Map[Decide, Map[H,CriticalPoints]];
Table[{CriticalPoints[[i]],Analysis[[i]]},{i,Length[CriticalPoints]}]
Here is a much slicker code, doing the same and even presenting it as a nice
table (credit: Matt Leingang, 2006)
ClassifyCriticalPoints[f_,{x_,y_}] := Module[{X,P,H,g,d,S},
X={x,y}; P=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} /. Sort[P],TableHeadings->{None,{x,y,"D","f_xx","Type","f"}}]]
ClassifyCriticalPoints[4 x y - x^3 y - x y^3,{x,y}]
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| 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 |
| ContourPlot[ Sin[x y],{x,-2,2},{y,-2,2} ] | Contour lines (traces) |
| Integrate[ x Sin[x], x] | Integrate symbolically |
| 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 |
Get["Graphics`ContourPlot3D`"];
ContourPlot3D[x^2+2y^2-z^2-1,{x,-2,2},{y,-2,2},{z,-2,2}] | Implicit surface |
| | Printing problems |
- I tried to print my notebook but there is no printout.
- Check your printing budget. The printer would spit out a page, which tells you this.
- You might have written the notebook to a PS file on your computer instead of sending it
to the printer (you can chose so at the printing dialog box).
- I want to save paper. How do I print out only a part of the notebook.
- Chose "print selection" instead of "print" in the Mathematica notebook. The selected cells will be printed.
- Alternatively, open a new notebook, cut and paste the part you need to turn in into
the new notebook and print that out.
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