Spring 2003

# Mathematics Math21a Spring 2003

## Multivariable Calculus

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

Availability Mathematica is installed on many Computers in the basement of the Science center. It might also be installed on the computers in the houses. If you want to try installation of mathematica on any of the Harvard computers, start here.
Getting the notebook Get it here , save it on your disc and import it to mathematica.
Running mathematica Mathematica is started like any other application on Macintoshs or PC's. On Unix, 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)
 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.