Maple #2 is a 5 part problem set. (Each part is worth 4 points for a total
of 20 points.)

parts C, D & E are due stapled together on Tuesday 14 Oct

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

You are to plot the five functions below (one for each part). 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. Most plotting commands are
loaded went you type with(plots);]

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).



C. A similar combined contour and gradplot for the function sin(x)+sin(y)
over one period in both the x and y direction. Like you did for parts A
and B. Avoid the zero contour (see part B). Note I only want to see one plot.
Don't forget scaling.

D. (Roughly #10 on test2 for fall02) Plot the z=1 contour for
g(x,y)=x^2+xy+y^2 and on the same graph plot several contour lines
for f(x,y)=x+y. Be sure to pick contours which include the minimum
and maximum values of f(x,y) subject to the constraint g(x,y)=1.
Don't forget scaling.

E. Display four graphs together. The first is a contourplot3d of the 
matlab function with the same -3..3 range as last week. The other 3
are spacecurve plots. The
spacecurves are determined by the cross-sections x=1 and y=2
and x-y=-1. Use thickness=3 and color=red (x=1), green (y=2) and
blue (x-y=-1). Don't forget the axes or a title.

As a shortcut the curves you want are (maple commands almost)
curve:=[x,y,matlab];
a:=spacecurve(eval(curve,x=1),y=-3..3,color=red, ... ):
b:=spacecurve(eval(curve,y=2),x=-3..3,color=green, ... ):
c:=spacecurve(eval(curve,y=1+x),x=-3..2,color=blue, ... ):
                                      ^             ^^^
                                      |             other options
                                      2 instead of 3 so that y=1+x <= 3.

Remember to orientate this display so that all the curves look like
curves and not straight lines. Note I want to see only one plot for part E.