Project 3 due 18 Sept.

FINAL COPY

STABLE your sheets together.
Your name at the top of the sheet (Insert Text)
Graphics must have your name in the title and include axes.
Graphics must be "nice" and rotated to a good view.
Be sure to answer any questions (Insert Text).
No smartplots.


1. Contourplot of the function (its definition takes two lines)
g(x,y)= 3*(1-x)^2*exp(-x^2-(y+1)^2)
        - 10*(x/5-x^3-y^5)*exp(-x^2-y^2) -(1/3)*exp(-(x+1)^2-y^2)
2. Contourplot function sin(e^x+e^y) for (x,y) in [0,3]x[0,3].
Increase the number of samples so the graph looks smooth.
3. Do a contourplot of both xy and x^2-y^2 on the same graph, make
it do at least 16 contours. (-a..a is a good range -- try a couple,
pick the best.)
4. Cylinder co-ordinates r = 1 + z sin(theta) for z in [0,2]. (Careful!
Try rearranging the order of theta=0..2*Pi and z=0..2, be sure to get
the correct one.) [A polar plot could help.]
5. Spherical coordinates, pho = sin(phi)*(1+theta). Theta and phi
have natural ranges -- be sure to get the order correct. After the
natural range, try it with theta going around twice. (Cut it in
half, or use wireframe style or something to show the otherwise
hidden part.)