Mathematics Maths21A Summer 2007

Multivariable Calculus

CAS

by Oliver Knill

Office: SciCtr 434

Email: knill@math.harvard.edu

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.
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Getting the notebook |
- The Mathematica laboratory is here. You can see a HTML preview of the unevaluated and evaluted notebook.
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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: |
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}] |

Please send questions and comments to maths21a@fas.harvard.edu

Maths21A | Oliver Knill | Summer 2007 |
Summer school |
Department of Mathematics |
Faculty of Art and Sciences |
Harvard University