## Mathematica Laboratory

The Mathematica project is due on July 30, 2016, stamp of the email. The Mathematica project is

## here.

Availability The Mathematica program can be obtained here. You can also Start here to register. After creating and validating your Wolfram account, sign in to the Wolfram User Portal and complete the Wolfram Activation Key Request Form. When selecting a product on the form, choose a version of "Mathematica for sites (single machine)." Click Submit. An activation key will be generated and emailed to you. Click the link for "Product Summary page". Click "Get Downloads" and select "Download" next to the appropriate platform. Follow the installation instructions and enter the activation key when prompted. The current version is Mathematica 10. During installation you will be prompted for an Activation Key. Send me an email if you plan to use Mathematica on a linux system.
Getting the notebook
Running Mathematica Mathematica starts like any other application on OS X or Windows. On Linux, type "mathematica" in a terminal to start the notebook version, or "math" if you want to use the terminal version.
Some basic 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 SphericalPlot3D[(2+Sin[2 t] Sin[3 s]),{t,0,Pi},{s,0,2 Pi}] Spherical Plot RevolutionPlot3D[{2 + Cos[t], t}, {t,0,2 Pi}] Revolution Plot ContourPlot[Sin[x y],{x,-2,2},{y,-2,2} ] Contour lines (traces) ContourPlot3D[x^2+2y^2-z^2,{x,-2,2},{y,-2,2},{z,-2,2}] Implicit surface VectorPlot[{x-y,x+y},{x,-3,3},{y,-3,3}] Vectorfield plot VectorPlot3D[{x-y,x+y,z},{x,-3,3},{y,-3,3},{z,0,1}] Vectorfield plot 3D Integrate[x Sin[x], x] Integrate symbolically Integrate[x y^2-z,{x,0,2},{y,0,x},{z,0,y}] 3D Integral 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 DSolve[{D[u[x,t],t]==D[u[x,t],x],u[x,0]==Sin[x]},u[x,t],{x,t}] Solution to PDE
Classify extrema:
```ClassifyCriticalPoints[f_,{x_,y_}]:=Module[{X,P,H,g,d,S}, X={x,y};
```F[x_,y_]:=2x^2+4 x y;     G[x_,y_]:=x^2 y;
```f[t_,x_]:=(x/t)*Sqrt[1/t]*Exp[-x^2/(4 t)]/(1+ Sqrt[1/t] Exp[-x^2/(4 t)]);