Maple #9 is due Tuesday 5 December 2000 

For FULL credit STAPLE your sheets together.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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. Be sure to answer the questions
in 4.

1&2 Plot the following surfaces from u=0..2, v=0..4 (from test 3 fall 98)
Each plot is separate.
  1a. <cos v, sin v, u>
  1b. <(2+u)cos 2v, (2+u)sin 2v, v>
  2a. <u cos v, u sin v, u>
  2b. <sin u cos v, sin u sin v, cos u>

3&4.  Line integrals. Use maple to draw  curtain plots like in the
maple worksheet of November 15' (or see below).
Eventually each line integral over a curve C reduces to integrating a
function like int(g(t),t=a..b). What we want is a `curtain' of height
g(t) over the curve C. If C is given by <x(t), y(t)>, t=a..b then
we want to plot the surface <x(t), y(t), s*g(t)> t=a..b, s=0..1.
We can do this with plot3d as follows
plot3d([x(t),y(t),s*g(t)],t=a..b,s=0..1,title=`line curtain`,axes=BOXED);
#3. Draw the curtain for #2 in 18.2 of the text
#4. Draw the curtain for #3 in 18.2 of the text.

5.  Plot a Klein bottle. The following should help. The handle and
bulb `fit together' to make one smooth surface.
c:=.6;a:=.2;
plot1 the handle:
Range u=Pi/2..5*Pi/2,v=Pi/4..5*Pi/4
A:=c*(cos(v)*sin(v) -0.5 + a*sin(u)*sin(v)/sqrt(sin(v)^2+cos(2*v)^2));
B:=a*c*cos(u);
C:=cos(v)+a*c*sin(u)*cos(2*v)/sqrt(sin(v)^2+cos(2*v)^2);
parametric equations of this part of the surface [A, B, C]

plot2 the bulb: v=5*Pi/4..9*Pi/4
Range u=Pi/2..5*Pi/2,v=5*Pi/4..9*Pi/4
r:=sin(v)*cos(v) - (a+1/2);
A:=c* sin(u) * r;
B:= -c * cos(u) * r;
C:=cos(v);
parametric equations of this part of the surface [A, B, C]