Summer 2003

# Mathematics Maths21a Summer 2003

## Multivariable Calculus

Office: SciCtr 434
Email: knill@math.harvard.edu
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## Mathematica Laboratory

Doing a Mathematica project is an option for a project.

 Visit the Gallery of Summer 2003!

Availability
• Mathematica is installed on some computers in the basement of the Science center.
• It might already be installed on the computer you use in the the houses.
• For an installation of Mathematica on your own machine, start here.
Getting the Assignment The assignment can be downloaded here. Once you have it on your machine, open the document from within mathematica. You can also click on the icon if you work on a PC or Mac which has Mathematica installed and knows the .nb extension. All the necessary information for doing the assignment is on that notebook.
Running mathematica Mathematica is started like any other application on Macintoshs or PC's. On Unix or linux, just type "mathematica" to start the notebook version, or "math" to start the terminal version. In OSX, it is a good idea to have the Mathematica icon available on the doc, on a PC, you might want to make a shortcut to the desctop.
Some frequently used commands are shown to the right. ( See more what you can do with Mathematica).
 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 See the Printing guide of HASCS. Note that you need to have a printing budget .
Printing problems
• I tried to print my notebook but there is no printout.
1. You might have no printing budget. The printer would spit out a page telling this.
2. 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.
1. Chose "print selection" instead of "print" in the Mathematica notebook. The selected cells will be printed.
2. Alternatively, open a new notebook, cut and paste the part you need to turn in into the new notebook and print that out.