Maths21a, Summer 2007, Multivariable Calculus,

Mathematica Laboratory

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. The current version is Mathematica 6. You need this version to do the assigment. 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. We will use Mathematica 6 this summer, which has exciting new features, like interactivity, opacity and animation.

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 maths21a, if you plan to use Mathematica on a linux system.

Getting the notebook

The Mathematica laboratory is here. You can see a HTML preview of the unevaluated and evaluted notebook.

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:

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

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}]