Project #4 is due Thursday 6 Feb 2003

This is an individual project with a separate evaluation sheet
on how the group of just you and maple got along.

For FULL credit STAPLE your sheets together.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Actually unstapled assignments will not be accepted.

You are to plot the five functions below. Each plot must be rotated to 
a "nice" position and "look good (smooth)" . Each plot must have include
axes and the title must include your name and what was plotted. Note
that the expressions below are not necessarily in a form that Maple
likes. 

[Remember, either define e:=exp(1) or replace e^x with exp(x). A common
error is to replace e^x with exp^x, and unfortunately Maple doesn't
notice the error, and does something dumb.]

The MATLAB function is given below, it has missing *'s and e's don't work
in Maple

matlab:= 3(1-x)^2 e^(-x^2-(y+1)^2)
    - 10(x/5-x^3-y^5)e^(-x^2-y^2) -(1/3)e^(-(x+1)^2-y^2).

1. Do a plot3d of the matlab function above use the following options to
the plot3d command fix the MISSING-STUFF and update YOUR-NAME and
WHAT-GRAPH.

plot3d(MISSING-STUFF,axes=boxed,shading=zhue,orientation=[-145,50],
title="YOUR-NAME and WHAT-GRAPH");

so that it matches the graph on the web:
http://www.math.fsu.edu/~bellenot/class/s03/cal3/maple/graph4_0.gif

(note: if it doesn't match you need to fix the function. The x
and y RANGE MUST MATCH the graph on the web.)

2. Do a plot3d of the matlab function over the same range but using
the style patch and contour instead of the default patch, if you 
use the default graph the contours don't look so good. Increase the
number of samples via grid or numpoints so the contours look smooth.
Remember the title.

3. Do a contourplot of the matlab function over the same range.
(contourplot NOT contourplot3d).  You need to both increase the number
of samples to make the contours smooth and increase the number of
contours to 20 (hint: contours=20).

4. Do a gradplot of the matlab function over the same range, using
the option arrows=thick (gradplot not gradplot3d).

5. Display the graphs in #3 and #4 together using the display funtion.
The arrows should cross the contours more or less perpendicular and
always point "uphill". The "size" of the arrow is proportional to
the steepest of the surface.